diff --git a/.github/workflows/build_book.yml b/.github/workflows/build_book.yml
index 62643703..1697a293 100644
--- a/.github/workflows/build_book.yml
+++ b/.github/workflows/build_book.yml
@@ -11,73 +11,56 @@ concurrency:
   group: ${{ github.ref }}  # Group runs by the ref (branch or PR)
   cancel-in-progress: true  # Cancel any ongoing runs in the same group
 
-defaults:
-  run:
-    working-directory: ./book
-
 jobs:
   build:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
-      - name: Install elan
-        run: curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh -s -- -y
-      # The build directories for analysis/ and book/ are cached separately, because they
-      # use disjoint sets of build dependencies. There's no need to rebuild both completely
-      # when only one has a version bump.
-      - name: Restore cache if available
-        uses: actions/cache/restore@v4
+
+      - uses: leanprover/lean-action@v1
         with:
-          path: |
-            ./analysis/.lake
-          key: lake-${{ runner.os }}-${{ runner.arch}}-${{ hashFiles('analysis/lean-toolchain') }}-${{ hashFiles('analysis/lake-manifest.json') }}-${{ github.sha }}
-          restore-keys: lake-${{ runner.os }}-${{ runner.arch}}-${{ hashFiles('analysis/lean-toolchain') }}-${{ hashFiles('analysis/lake-manifest.json') }}
-      - name: Restore book cache if available
+          build: false
+          test: false
+          use-mathlib-cache: true
+          use-github-cache: false
+      # We manage the Lake cache ourselves rather than using
+      # lean-action's built-in caching because lean-action saves the
+      # cache before we generate the site. As a result, Verso and its
+      # HTML artifacts would never be cached.
+      - name: Restore Lake cache
         uses: actions/cache/restore@v4
         with:
-          path: |
-            ./book/.lake
-          key: lake-${{ runner.os }}-${{ runner.arch}}-${{ hashFiles('book/lean-toolchain') }}-${{ hashFiles('book/lake-manifest.json') }}-${{ github.sha }}
-          restore-keys: lake-${{ runner.os }}-${{ runner.arch}}-${{ hashFiles('book/lean-toolchain') }}-${{ hashFiles('book/lake-manifest.json') }}
-
-      # Getting the mathlib cache is only useful when mathlib gets updated, but will save a lot of time in that case.
-      - name: Get Mathlib cache
-        run: ~/.elan/bin/lake exe cache get || true
-        working-directory: ./analysis
+          path: .lake
+          key: lake-${{ runner.os }}-${{ runner.arch }}-${{ hashFiles('lean-toolchain') }}-${{ hashFiles('lake-manifest.json') }}-${{ github.sha }}
+          restore-keys: lake-${{ runner.os }}-${{ runner.arch }}-${{ hashFiles('lean-toolchain') }}-${{ hashFiles('lake-manifest.json') }}
+      - name: Build project
+        run: lake build
       - name: Build doc-gen
-        run: ~/.elan/bin/lake -R -Kenv=dev build Analysis:docs
-        working-directory: ./analysis
-      - name: Build metadata of project
-        run: ~/.elan/bin/lake build
-        working-directory: ./analysis
+        run: lake -R -Kenv=dev build Analysis:docs
       - name: Build book
+        id: build-site
         run: |
-          ~/.elan/bin/lake exe analysis-book 
-      - name: Copy docs to analysis-book
-        run: |
-          cp -r ../analysis/.lake/build/doc _site/docs
-      - name: Remove unnecessary lake files from documentation in `_site/docs`
+          SITE_PATH="$(lake query :literateHtml)"
+          echo "Generated site at: $SITE_PATH"
+          echo "path=$SITE_PATH" >> "$GITHUB_OUTPUT"
+          mkdir -p _site
+          cp -r "$SITE_PATH/." _site
+      - name: Copy docs to site
+        run: cp -r .lake/build/doc _site/docs
+      - name: Remove unnecessary Lake files from docs
         run: |
           find _site/docs -name "*.trace" -delete
           find _site/docs -name "*.hash" -delete
-      # The cache for analysis/ is saved here, rather than before building the book, because
-      # building the book generates JSON files full of literate program artifacts in analysis/.lake
-      - name: Save cache
-        uses: actions/cache/save@v4
-        with:
-          path: |
-            ./analysis/.lake
-          key: lake-${{ runner.os }}-${{ runner.arch}}-${{ hashFiles('analysis/lean-toolchain') }}-${{ hashFiles('analysis/lake-manifest.json') }}-${{ github.sha }}
-      - name: Save book cache
+      - name: Save Lake cache
+        if: always()
         uses: actions/cache/save@v4
         with:
-          path: |
-            ./book/.lake
-          key: lake-${{ runner.os }}-${{ runner.arch}}-${{ hashFiles('book/lean-toolchain') }}-${{ hashFiles('book/lake-manifest.json') }}-${{ github.sha }}
+          path: .lake
+          key: lake-${{ runner.os }}-${{ runner.arch }}-${{ hashFiles('lean-toolchain') }}-${{ hashFiles('lake-manifest.json') }}-${{ github.sha }}
       - name: Upload website
         uses: actions/upload-pages-artifact@v3
         with:
-          path: './book/_site'
+          path: _site
   deploy:
     # Add a dependency to the build job
     needs: build
diff --git a/.github/workflows/check-version-consistency.yml b/.github/workflows/check-version-consistency.yml
deleted file mode 100644
index 64a48bc7..00000000
--- a/.github/workflows/check-version-consistency.yml
+++ /dev/null
@@ -1,86 +0,0 @@
-name: Validate Subverso Package Hashes
-
-on:
-  push:
-  pull_request:
-
-jobs:
-  validate-json:
-    runs-on: ubuntu-latest
-    
-    steps:
-    - name: Checkout repository
-      uses: actions/checkout@v4
-      
-    - name: Validate subverso package hashes
-      run: |
-        set -e
-        
-        echo "Checking expected version from book/lake-manifest.json..."
-        
-        # Get expected version from the primary file
-        if ! expected_version=$(jq -r '.packages[] | select(.name == "subverso") | .rev' book/lake-manifest.json 2>/dev/null); then
-          echo "::error::Failed to extract SubVerso hash from book/lake-manifest.json"
-          echo "::error::This means the respository structure has changed and this script needs updating."
-          exit 1
-        fi
-        
-        # Check if the result is non-empty
-        if [[ -z "$expected_version" || "$expected_version" == "null" ]]; then
-          echo "::error::No subverso package found or empty hash in book/lake-manifest.json"
-          echo "::error::This means the respository structure has changed and this script needs updating."
-          exit 1
-        fi
-        
-        echo "Expected version: $expected_version"
-        
-        echo "Finding all lake-manifest.json files..."
-        manifest_files=$(find . -name "lake-manifest.json" -type f)
-        
-        if [[ -z "$manifest_files" ]]; then
-          echo "::error::No lake-manifest.json files found in repository"
-          echo "::error::This means the respository structure has changed and this script needs updating."
-          exit 1
-        fi
-        
-        echo "Found files:"
-        echo "$manifest_files"
-        echo ""
-        
-        # Check each manifest file
-        exit_code=0
-        
-        while IFS= read -r file; do
-          echo "Checking $file..."
-          
-          if ! current_hash=$(jq -r '.packages[] | select(.name == "subverso") | .rev' "$file" 2>/dev/null); then
-            echo "::error::Failed to extract subverso hash from $file"
-            exit_code=1
-            continue
-          fi
-          
-          if [[ -z "$current_hash" || "$current_hash" == "null" ]]; then
-            echo "::error::No subverso package found or empty hash in $file"
-            exit_code=1
-            continue
-          fi
-          
-          if [[ "$current_hash" != "$expected_version" ]]; then
-            echo "::error::Hash mismatch in $file"
-            echo "::error::Expected: $expected_version"
-            echo "::error::Found: $current_hash"
-            exit_code=1
-          else
-            echo "✓ Hash matches: $current_hash"
-          fi
-        done <<< "$manifest_files"
-        
-        if [[ $exit_code -ne 0 ]]; then
-          echo ""
-          echo "::error::Mismatched versions of SubVerso. Please run ./sync-versions.sh in the respository"
-          echo "::error::root to fix the situation."
-          exit 1
-        fi
-        
-        echo ""
-        echo "✓ All SubVerso package hashes match across all lake-manifest.json files"
diff --git a/.gitignore b/.gitignore
index 050d947d..ed0ed491 100644
--- a/.gitignore
+++ b/.gitignore
@@ -16,7 +16,7 @@ _site/
 .claude/
 .cursor/
 Claude.md
-analysis/.repair
+.repair
 **/.env
 **/.aider.conf.yml
 **/.formalize
diff --git a/analysis/Analysis.lean b/Analysis.lean
similarity index 50%
rename from analysis/Analysis.lean
rename to Analysis.lean
index b40a14d3..1cdce771 100644
--- a/analysis/Analysis.lean
+++ b/Analysis.lean
@@ -97,3 +97,21 @@ import Analysis.MeasureTheory.Section_1_3_2
 import Analysis.MeasureTheory.Section_1_3_3
 import Analysis.MeasureTheory.Section_1_3_4
 import Analysis.MeasureTheory.Section_1_3_5
+
+/-!
+ The files in this directory contain a formalization of selected portions of my text [Analysis I](https://terrytao.wordpress.com/books/analysis-i/) into [Lean](https://lean-lang.org/). The formalization is intended to be as faithful a paraphrasing as possible to the original text, while also showcasing Lean's features and syntax. In particular, the formalization is not optimized for efficiency, and in some cases may deviate from idiomatic Lean usage.
+
+Portions of the text that were left as exercises to the reader are rendered in this translation as sorrys. Readers are welcome to fork the repository here to try their hand at these exercises, but I do not intend to place solutions in this repository directly.
+
+While the arrangement of definitions, theorems, and proofs here are closely paraphrasing the textbook, I am refraining from directly quoting material from the textbook, instead providing references to the original text where appropriate. As such, this formalization should be viewed as an annotated companion to the primary text, rather than a replacement for it.
+
+Much of the material in this text is duplicated in Lean's standard math library [Mathlib](https://leanprover-community.github.io/mathlib4_docs/), though with slightly different definitions. To reconcile these discrepancies, this formalization will gradually transition from the textbook-provided definitions to the Mathlib-provided definitions as one progresses further into the text, thus sacrificing the self-containedness of the formalization in favor of compatibility with Mathlib. For instance, Chapter 2 develops a theory of the natural numbers independent of Mathlib, but all subsequent chapters will use the Mathlib natural numbers instead. (An epilogue to Chapter 2 is provided to show that the two notions of the natural numbers are isomorphic.) As such, this formalization can also be used as an introduction to various portions of Mathlib.
+
+In order to align the formalization with Mathlib conventions, a small number of technical changes have been made to some of the definitions as compared with the textbook version. Most notably:
+
+    Sequences are indexed to start from zero rather than from one, as Mathlib has much more support for the 0-based natural numbers ℕ than the 1-based natural numbers.
+
+    Many operations that are left undefined in the text, such as division by zero, or taking the formal limit of a non-Cauchy sequence, are instead assigned a "junk" value (e.g., 0) to make the operation totally defined. This is because Lean has better support for total functions than partial functions (indiscriminate use of the latter can lead into "dependent type hell" in which even very basic manipulations require quite subtle and delicate proofs). See for instance [this blog post](https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-theory-a-faq/) by Kevin Buzzard for more discussion.
+
+[*Generated documentation*](docs/) is available for the project and its dependencies.
+-/
diff --git a/analysis/Analysis/Appendix_A_1.lean b/Analysis/Appendix_A_1.lean
similarity index 94%
rename from analysis/Analysis/Appendix_A_1.lean
rename to Analysis/Appendix_A_1.lean
index f9bb9c83..cba37ad1 100644
--- a/analysis/Analysis/Appendix_A_1.lean
+++ b/Analysis/Appendix_A_1.lean
@@ -186,14 +186,14 @@ example {X Y Z:Prop} (hXY: X ↔ Y) (hXZ: X ↔ Z) : [X,Y,Z].TFAE := by
   tfae_have 1 ↔ 3 := by exact hXZ  -- This line is optional
   tfae_finish
 
-/-- Note for the `.out` method that one indexes starting from 0, in contrast to the `tfae_have` tactic. -/
+/-- Note for the {name (full := List.TFAE.out)}`out` method that one indexes starting from 0, in contrast to the {tactic}`tfae_have` tactic. -/
 example {X Y Z:Prop} (h: [X,Y,Z].TFAE) : X ↔ Y := by
   exact h.out 0 1
 
-/-- Exercise A.1.1.  Fill in the first `sorry` with something reasonable. -/
+/-- Exercise A.1.1.  Fill in the first {syntax term}`sorry` with something reasonable. -/
 example {X Y:Prop} : ¬ ((X ∨ Y) ∧ ¬ (X ∧ Y)) ↔ sorry := by sorry
 
-/-- Exercise A.1.2.  Fill in the first `sorry` with something reasonable. -/
+/-- Exercise A.1.2.  Fill in the first {syntax term}`sorry` with something reasonable. -/
 example {X Y:Prop} : ¬ (X ↔ Y) ↔ sorry := by sorry
 
 /-- Exercise A.1.3. -/
diff --git a/analysis/Analysis/Appendix_A_2.lean b/Analysis/Appendix_A_2.lean
similarity index 100%
rename from analysis/Analysis/Appendix_A_2.lean
rename to Analysis/Appendix_A_2.lean
diff --git a/analysis/Analysis/Appendix_A_3.lean b/Analysis/Appendix_A_3.lean
similarity index 100%
rename from analysis/Analysis/Appendix_A_3.lean
rename to Analysis/Appendix_A_3.lean
diff --git a/analysis/Analysis/Appendix_A_4.lean b/Analysis/Appendix_A_4.lean
similarity index 100%
rename from analysis/Analysis/Appendix_A_4.lean
rename to Analysis/Appendix_A_4.lean
diff --git a/analysis/Analysis/Appendix_A_5.lean b/Analysis/Appendix_A_5.lean
similarity index 100%
rename from analysis/Analysis/Appendix_A_5.lean
rename to Analysis/Appendix_A_5.lean
diff --git a/analysis/Analysis/Appendix_A_6.lean b/Analysis/Appendix_A_6.lean
similarity index 100%
rename from analysis/Analysis/Appendix_A_6.lean
rename to Analysis/Appendix_A_6.lean
diff --git a/analysis/Analysis/Appendix_A_7.lean b/Analysis/Appendix_A_7.lean
similarity index 100%
rename from analysis/Analysis/Appendix_A_7.lean
rename to Analysis/Appendix_A_7.lean
diff --git a/analysis/Analysis/Appendix_B_1.lean b/Analysis/Appendix_B_1.lean
similarity index 98%
rename from analysis/Analysis/Appendix_B_1.lean
rename to Analysis/Appendix_B_1.lean
index 29899ad1..80afb684 100644
--- a/analysis/Analysis/Appendix_B_1.lean
+++ b/Analysis/Appendix_B_1.lean
@@ -3,9 +3,9 @@ import Mathlib.Tactic
 /-!
 # Analysis I, Appendix B.1: The decimal representation of natural numbers
 
-Am implementation of the decimal representation of Mathlib's natural numbers `ℕ`.
+Am implementation of the decimal representation of Mathlib's natural numbers {lean}`ℕ`.
 
-This is separate from the way decimal numerals are already represenated in Mathlib via the `OfNat` typeclass.
+This is separate from the way decimal numerals are already represenated in Mathlib via the {name}`OfNat` typeclass.
 -/
 
 namespace AppendixB
@@ -154,7 +154,7 @@ theorem PosintDecimal.pos (p:PosintDecimal) : 0 < (p:ℕ) := by
 abbrev PosintDecimal.append (p:PosintDecimal) (d:Digit) : PosintDecimal :=
   mk' p.head (p.digits.tail ++ [d]) p.head_ne_zero
 
-/-- `toNat` equals Horner (left-fold) evaluation of the digit list. -/
+/-- {name}`toNat` equals Horner (left-fold) evaluation of the digit list. -/
 theorem PosintDecimal.toNat_eq_foldl (q : PosintDecimal) :
     q.toNat = q.digits.foldl (fun acc (d : Digit) => acc * 10 + d.toNat) 0 := by
   suffices h : ∀ (L : List Digit) (acc : ℕ),
diff --git a/analysis/Analysis/Appendix_B_2.lean b/Analysis/Appendix_B_2.lean
similarity index 96%
rename from analysis/Analysis/Appendix_B_2.lean
rename to Analysis/Appendix_B_2.lean
index 59e57e61..2910da9e 100644
--- a/analysis/Analysis/Appendix_B_2.lean
+++ b/Analysis/Appendix_B_2.lean
@@ -4,10 +4,10 @@ import Analysis.Appendix_B_1
 /-!
 # Analysis I, Appendix B.2: The decimal representation of real numbers
 
-An implementation of the decimal representation of Mathlib's real numbers `ℝ`.
+An implementation of the decimal representation of Mathlib's real numbers {lean}`ℝ`.
 
-This is separate from the way decimal numerals are already represented in Mathlib.  We also represent the integer part of the natural numbers just by `ℕ`, avoiding using the decimal representation from the
-previous section, although we still retain the `Digit` class.
+This is separate from the way decimal numerals are already represented in Mathlib.  We also represent the integer part of the natural numbers just by {lean}`ℕ`, avoiding using the decimal representation from the
+previous section, although we still retain the {name}`AppendixB.Digit` class.
 -/
 
 namespace AppendixB
diff --git a/analysis/Analysis/MeasureTheory/Notation.lean b/Analysis/MeasureTheory/Notation.lean
similarity index 97%
rename from analysis/Analysis/MeasureTheory/Notation.lean
rename to Analysis/MeasureTheory/Notation.lean
index 9e0c0050..afd56e4b 100644
--- a/analysis/Analysis/MeasureTheory/Notation.lean
+++ b/Analysis/MeasureTheory/Notation.lean
@@ -5,12 +5,12 @@ import Mathlib.Tactic
 
 A companion to Chapter 0 of the book "An introduction to Measure Theory".
 
-We use existing Mathlib constructions, such as `Set.indicator`, `EuclideanSpace`, `ENNReal`,
-and `tsum` to describe the concepts defined in Chapter 0.
+We use existing Mathlib constructions, such as {name}`Set.indicator`, {name}`EuclideanSpace`, {name}`ENNReal`,
+and {name}`tsum` to describe the concepts defined in Chapter 0.
 
 -/
 
-/-- A version of `Set.indicator` suitable for this text. -/
+/-- A version of {name}`Set.indicator` suitable for this text. -/
 noncomputable abbrev Set.indicator' {X: Type*} (E: Set X) := indicator E (fun _ ↦ (1:ℝ))
 
 theorem Set.indicator'_apply {X: Type*} (E: Set X) (x: X) [Decidable (x ∈ E)] : indicator' E x = if x ∈ E then 1 else 0 := indicator_apply _ _ _
@@ -21,7 +21,7 @@ theorem Set.indicator'_of_mem {X: Type*} {E:Set X} {x:X} (h: x ∈ E) : indicato
 theorem Set.indicator'_of_notMem {X: Type*} {E:Set X} {x:X} (h: x ∉ E) : indicator' E x = 0 :=
   indicator_of_notMem h _
 
-/-- A version of `EuclideanSpace` suitable for this text. -/
+/-- A version of {name}`EuclideanSpace` suitable for this text. -/
 noncomputable abbrev EuclideanSpace' (n: ℕ) := EuclideanSpace ℝ (Fin n)
 
 abbrev EuclideanSpace'.equiv_Real : EuclideanSpace' 1 ≃ ℝ where
diff --git a/analysis/Analysis/MeasureTheory/README.md b/Analysis/MeasureTheory/README.md
similarity index 86%
rename from analysis/Analysis/MeasureTheory/README.md
rename to Analysis/MeasureTheory/README.md
index dfbf578f..908acaa4 100644
--- a/analysis/Analysis/MeasureTheory/README.md
+++ b/Analysis/MeasureTheory/README.md
@@ -8,29 +8,29 @@ Some of the material in this text is duplicated in Lean's standard math library
 
 ## Sections (work in progress)
 
-- Notation section ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Notation.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Notation.lean))
+- Notation section ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Notation.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Notation.lean))
 - Chapter 1: Measure Theory
   - Section 1.1: Prologue: the problem of measure
-    - Section 1.1.1: Elementary measure ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_1_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_1_1.lean))
-    - Section 1.1.2: Jordan measure ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_1_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_1_2.lean))
-    - Section 1.1.3: Connections with the Riemann integral ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_1_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_1_3.lean))
+    - Section 1.1.1: Elementary measure ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_1_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_1_1.lean))
+    - Section 1.1.2: Jordan measure ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_1_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_1_2.lean))
+    - Section 1.1.3: Connections with the Riemann integral ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_1_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_1_3.lean))
   - Section 1.2: Lebesgue measure
-    - Introduction: ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_2.lean))
-    - Section 1.2.1: Properties of Lebesgue outer measure ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_2_1.lean))
-    - Section 1.2.2: Lebesgue measurability ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_2_2.lean))
-    - Section 1.2.3: Non-measurable sets ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_2_3.lean))
+    - Introduction: ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_2.lean))
+    - Section 1.2.1: Properties of Lebesgue outer measure ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_2_1.lean))
+    - Section 1.2.2: Lebesgue measurability ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_2_2.lean))
+    - Section 1.2.3: Non-measurable sets ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_2_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_2_3.lean))
   - Section 1.3: The Lebesgue integral
-    - Section 1.3.1: Integration of simple functions ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_3_1.lean))
-    - Section 1.3.2: Measurable functions ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_3_2.lean))
-    - Section 1.3.3: Unsigned Lebesgue integrals ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_3_3.lean))
-    - Section 1.3.4: Absolute integrability ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_3_4.lean))
-    - Section 1.3.5: Littlewood's three principles ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_3_5.lean))
+    - Section 1.3.1: Integration of simple functions ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_3_1.lean))
+    - Section 1.3.2: Measurable functions ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_3_2.lean))
+    - Section 1.3.3: Unsigned Lebesgue integrals ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_3_3.lean))
+    - Section 1.3.4: Absolute integrability ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_3_4.lean))
+    - Section 1.3.5: Littlewood's three principles ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_3_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_3_5.lean))
   - Section 1.4: Abstract measure spaces
-    - Section 1.4.1: Boolean algebras ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_4_1.lean))
-    - Section 1.4.2: $\sigma$-algebras and measurable spaces ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_4_2.lean))
-    - Section 1.4.3: Countably additive measures and measure spaces ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_4_3.lean))
-    - Section 1.4.4: Measurable functions, and integration on a measure space ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_4_4.lean))
-    - Section 1.4.5: The convergence theorems ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/MeasureTheory/Section_1_4_5.lean))
+    - Section 1.4.1: Boolean algebras ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_4_1.lean))
+    - Section 1.4.2: $\sigma$-algebras and measurable spaces ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_4_2.lean))
+    - Section 1.4.3: Countably additive measures and measure spaces ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_4_3.lean))
+    - Section 1.4.4: Measurable functions, and integration on a measure space ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_4_4.lean))
+    - Section 1.4.5: The convergence theorems ([Documentation](https://teorth.github.io/analysis/docs/Analysis/MeasureTheory/Section_1_4_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/MeasureTheory/Section_1_4_5.lean))
   - Section 1.5: Modes of convergence
     - Introduction: (Documentation) (Lean source)
     - Section 1.5.1: Uniqueness (Documentation) (Lean source)
diff --git a/analysis/Analysis/MeasureTheory/Section_1_1_1.lean b/Analysis/MeasureTheory/Section_1_1_1.lean
similarity index 96%
rename from analysis/Analysis/MeasureTheory/Section_1_1_1.lean
rename to Analysis/MeasureTheory/Section_1_1_1.lean
index 87b99172..8d498e4f 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_1_1.lean
+++ b/Analysis/MeasureTheory/Section_1_1_1.lean
@@ -19,7 +19,7 @@ inductive BoundedInterval where
 
 open BoundedInterval
 
-/-- Coerces a BoundedInterval to its underlying set of real numbers. -/
+/-- Coerces a {name}`BoundedInterval` to its underlying set of real numbers. -/
 @[coe]
 def BoundedInterval.toSet (I: BoundedInterval) : Set ℝ := match I with
   | Ioo a b => .Ioo a b
@@ -27,24 +27,24 @@ def BoundedInterval.toSet (I: BoundedInterval) : Set ℝ := match I with
   | Ioc a b => .Ioc a b
   | Ico a b => .Ico a b
 
-/-- Enables coercion from BoundedInterval to Set ℝ. -/
+/-- Enables coercion from {name}`BoundedInterval` to {lean}`Set ℝ`. -/
 instance BoundedInterval.inst_coeSet : Coe BoundedInterval (Set ℝ) where
   coe := toSet
 
-/-- The empty BoundedInterval is represented as the degenerate open interval (0,0). -/
+/-- The empty {name}`BoundedInterval` is represented as the degenerate open interval (0,0). -/
 instance BoundedInterval.instEmpty : EmptyCollection BoundedInterval where
   emptyCollection := Ioo 0 0
 
-/-- The empty BoundedInterval coerces to the empty set. -/
+/-- The empty {name}`BoundedInterval` coerces to the empty set. -/
 @[simp]
 theorem BoundedInterval.coe_empty : ((∅ : BoundedInterval):Set ℝ) = ∅ := by
   simp [toSet]
 
 open Classical in
-/-- This is to make Finsets of BoundedIntervals work properly -/
+/-- This is to make {name}`Finset`s of {name}`BoundedInterval`s work properly -/
 noncomputable instance BoundedInterval.decidableEq : DecidableEq BoundedInterval := instDecidableEqOfLawfulBEq
 
-/-- Simp lemmas for coercing each BoundedInterval constructor to Set ℝ. -/
+/-- Simp lemmas for coercing each {name}`BoundedInterval` constructor to {lean}`Set ℝ`. -/
 @[simp]
 theorem BoundedInterval.set_Ioo (a b:ℝ) : (Ioo a b : Set ℝ) = .Ioo a b := by rfl
 
@@ -57,7 +57,7 @@ theorem BoundedInterval.set_Ioc (a b:ℝ) : (Ioc a b : Set ℝ) = .Ioc a b := by
 @[simp]
 theorem BoundedInterval.set_Ico (a b:ℝ) : (Ico a b : Set ℝ) = .Ico a b := by rfl
 
-/-- Some helpful general lemmas about BoundedInterval -/
+/-- Some helpful general lemmas about {name}`BoundedInterval` -/
 theorem Bornology.IsBounded.of_boundedInterval (I: BoundedInterval) : Bornology.IsBounded (I:Set ℝ) := by
   cases I with
   | Ioo a b =>
@@ -75,7 +75,7 @@ theorem Bornology.IsBounded.of_boundedInterval (I: BoundedInterval) : Bornology.
 
 namespace BoundedInterval
 
-/-- Extract endpoints from Icc equality -/
+/-- Extract endpoints from {name}`BoundedInterval.Icc` equality -/
 lemma Icc_eq_endpoints {a₁ b₁ a₂ b₂ : ℝ}
     (h : Set.Icc a₁ b₁ = Set.Icc a₂ b₂) (ha₁b₁ : a₁ ≤ b₁) (ha₂b₂ : a₂ ≤ b₂) :
     a₁ = a₂ ∧ b₁ = b₂ := by
@@ -91,7 +91,7 @@ lemma Icc_eq_endpoints {a₁ b₁ a₂ b₂ : ℝ}
     rw [← h] at h₂; simp [Set.mem_Icc] at h₂
     linarith
 
-/-- Ioo cannot equal Icc -/
+/-- {name}`BoundedInterval.Ioo` cannot equal {name}`BoundedInterval.Icc` -/
 lemma Ioo_ne_Icc {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b₂ : a₂ ≤ b₂) :
     Set.Ioo a₁ b₁ ≠ Set.Icc a₂ b₂ := by
   intro h
@@ -103,7 +103,7 @@ lemma Ioo_ne_Icc {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b
   rw [← h] at this
   contradiction
 
-/-- Ioo cannot equal Ioc -/
+/-- {name}`BoundedInterval.Ioo` cannot equal {name}`BoundedInterval.Ioc` -/
 lemma Ioo_ne_Ioc {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b₂ : a₂ < b₂) :
     Set.Ioo a₁ b₁ ≠ Set.Ioc a₂ b₂ := by
   intro h
@@ -115,7 +115,7 @@ lemma Ioo_ne_Ioc {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b
   simp [Set.mem_Ioo] at this
   linarith
 
-/-- Ioo cannot equal Ico -/
+/-- {name}`BoundedInterval.Ioo` cannot equal {name}`BoundedInterval.Ico` -/
 lemma Ioo_ne_Ico {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b₂ : a₂ < b₂) :
     Set.Ioo a₁ b₁ ≠ Set.Ico a₂ b₂ := by
   intro h
@@ -127,7 +127,7 @@ lemma Ioo_ne_Ico {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b
   simp [Set.mem_Ioo] at this
   linarith
 
-/-- Ioc cannot equal Ico -/
+/-- {name}`BoundedInterval.Ioc` cannot equal {name}`BoundedInterval.Ico` -/
 lemma Ioc_ne_Ico {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b₂ : a₂ < b₂) :
     Set.Ioc a₁ b₁ ≠ Set.Ico a₂ b₂ := by
   intro h
@@ -139,7 +139,7 @@ lemma Ioc_ne_Ico {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ < b₁) (ha₂b
   simp [Set.mem_Ico] at this
   linarith
 
-/-- Icc cannot equal Ioc -/
+/-- {name}`BoundedInterval.Icc` cannot equal {name}`BoundedInterval.Ioc` -/
 lemma Icc_ne_Ioc {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ ≤ b₁) (ha₂b₂ : a₂ < b₂) :
     Set.Icc a₁ b₁ ≠ Set.Ioc a₂ b₂ := by
   intro h
@@ -151,7 +151,7 @@ lemma Icc_ne_Ioc {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ ≤ b₁) (ha₂b
   simp [Set.mem_Ioc] at this
   linarith
 
-/-- Icc cannot equal Ico -/
+/-- {name}`BoundedInterval.Icc` cannot equal {name}`BoundedInterval.Ico` -/
 lemma Icc_ne_Ico {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ ≤ b₁) (ha₂b₂ : a₂ < b₂) :
     Set.Icc a₁ b₁ ≠ Set.Ico a₂ b₂ := by
   intro h
@@ -163,31 +163,31 @@ lemma Icc_ne_Ico {a₁ b₁ a₂ b₂ : ℝ} (ha₁b₁ : a₁ ≤ b₁) (ha₂b
   simp [Set.mem_Ico] at this
   linarith
 
-/-- Extract that a < b from nonempty Ioo -/
+/-- Extract that a < b from nonempty {name}`BoundedInterval.Ioo` -/
 private lemma nonempty_Ioo_strictness {a b : ℝ} (h : (Ioo a b).toSet.Nonempty) : a < b := by
   obtain ⟨x, hx⟩ := h
   simp [toSet] at hx
   exact hx.1.trans hx.2
 
-/-- Extract that a < b from nonempty Ioc -/
+/-- Extract that a < b from nonempty {name}`BoundedInterval.Ioc` -/
 private lemma nonempty_Ioc_strictness {a b : ℝ} (h : (Ioc a b).toSet.Nonempty) : a < b := by
   obtain ⟨x, hx⟩ := h
   simp [toSet] at hx
   exact hx.1.trans_le hx.2
 
-/-- Extract that a < b from nonempty Ico -/
+/-- Extract that a < b from nonempty {name}`BoundedInterval.Ico` -/
 private lemma nonempty_Ico_strictness {a b : ℝ} (h : (Ico a b).toSet.Nonempty) : a < b := by
   obtain ⟨x, hx⟩ := h
   simp [toSet] at hx
   exact hx.1.trans_lt hx.2
 
-/-- Extract that a ≤ b from nonempty Icc -/
+/-- Extract that a ≤ b from nonempty {name}`BoundedInterval.Icc` -/
 private lemma nonempty_Icc_order {a b : ℝ} (h : (Icc a b).toSet.Nonempty) : a ≤ b := by
   obtain ⟨x, hx⟩ := h
   simp [toSet] at hx
   exact hx.1.trans hx.2
 
-/-- Extract equal endpoints from equal Icc sets -/
+/-- Extract equal endpoints from equal {name}`BoundedInterval.Icc` sets -/
 private lemma endpoints_of_Icc_eq {a₁ b₁ a₂ b₂ : ℝ}
     (h_closure : Set.Icc a₁ b₁ = Set.Icc a₂ b₂) (ha₁b₁ : a₁ ≤ b₁) (ha₂b₂ : a₂ ≤ b₂) :
     a₁ = a₂ ∧ b₁ = b₂ := by
@@ -203,7 +203,7 @@ private lemma endpoints_of_Icc_eq {a₁ b₁ a₂ b₂ : ℝ}
     rw [← h_closure] at h₂; simp [Set.mem_Icc] at h₂
     linarith
 
-/-- BoundedInterval.toSet is injective for non-empty intervals -/
+/-- {name}`BoundedInterval.toSet` is injective for non-empty intervals -/
 lemma toSet_injective_of_nonempty {I J : BoundedInterval}
     (hI : I.toSet.Nonempty) (hJ : J.toSet.Nonempty) (h_eq : I.toSet = J.toSet) :
     I = J := by
@@ -321,7 +321,7 @@ theorem sInf_lt_of_ne_sInf {X : Set ℝ} {a x : ℝ} (_hBddBelow : BddBelow X) (
     (ha_notin : a ∉ X) (hx : x ∈ X) (ha_le_x : a ≤ x) : a < x := by
   by_contra! h; exact ha_notin (h.antisymm ha_le_x ▸ hx)
 
-/-- Use order-connectedness to show x ∈ X when x ∈ [w, z] and w, z ∈ X -/
+/-- Use order-connectedness to show x ∈ X when x ∈ \[w, z\] and w, z ∈ X -/
 theorem mem_of_mem_Icc_ordConnected {X : Set ℝ}
     (hOrdConn : ∀ ⦃x : ℝ⦄, x ∈ X → ∀ ⦃y : ℝ⦄, y ∈ X → Set.Icc x y ⊆ X)
     {x w z : ℝ} (hw : w ∈ X) (hz : z ∈ X) (hx : x ∈ Set.Icc w z) : x ∈ X :=
@@ -455,29 +455,29 @@ theorem BoundedInterval.inter (I J: BoundedInterval) : ∃ K : BoundedInterval,
     exact Set.OrdConnected.inter hI_ordConn hJ_ordConn
   exact (BoundedInterval.ordConnected_iff ((I:Set ℝ) ∩ (J:Set ℝ))).mp ⟨hBounded, hOrdConn⟩
 
-/-- Instance enabling ∩ notation for BoundedIntervals. -/
+/-- Instance enabling ∩ notation for {name}`BoundedInterval`s. -/
 noncomputable instance BoundedInterval.instInter : Inter BoundedInterval where
   inter I J := (inter I J).choose
 
-/-- The intersection of BoundedIntervals equals the set-theoretic intersection. -/
+/-- The intersection of {name}`BoundedInterval`s equals the set-theoretic intersection. -/
 @[simp]
 theorem BoundedInterval.inter_eq (I J: BoundedInterval) : (I ∩ J : BoundedInterval) = (I:Set ℝ) ∩ (J:Set ℝ)  :=
   (inter I J).choose_spec.symm
 
-/-- Instance enabling ∈ notation for membership in BoundedInterval. -/
+/-- Instance enabling ∈ notation for membership in {name}`BoundedInterval`. -/
 instance BoundedInterval.instMembership : Membership ℝ BoundedInterval where
   mem I x := x ∈ (I:Set ℝ)
 
-/-- Membership in BoundedInterval is equivalent to membership in its underlying set. -/
+/-- Membership in {name}`BoundedInterval` is equivalent to membership in its underlying set. -/
 @[simp]
 theorem BoundedInterval.mem_iff (I: BoundedInterval) (x:ℝ) :
   x ∈ I ↔ x ∈ (I:Set ℝ) := by rfl
 
-/-- Instance enabling ⊆ notation for BoundedIntervals. -/
+/-- Instance enabling ⊆ notation for {name}`BoundedInterval`s. -/
 instance BoundedInterval.instSubset : HasSubset BoundedInterval where
   Subset I J := ∀ x, x ∈ I → x ∈ J
 
-/-- Subset of BoundedIntervals is equivalent to subset of their underlying sets. -/
+/-- Subset of {name}`BoundedInterval`s is equivalent to subset of their underlying sets. -/
 @[simp]
 theorem BoundedInterval.subset_iff (I J: BoundedInterval) :
   I ⊆ J ↔ (I:Set ℝ) ⊆ (J:Set ℝ) := by rfl
@@ -496,7 +496,7 @@ abbrev BoundedInterval.b (I: BoundedInterval) : ℝ := match I with
   | Ioc _ b => b
   | Ico _ b => b
 
-/-- Any nonempty BoundedInterval has a ≤ b -/
+/-- Any nonempty {name}`BoundedInterval` has a ≤ b -/
 lemma BoundedInterval.nonempty_implies_le (I : BoundedInterval) (h : I.toSet.Nonempty) : I.a ≤ I.b := by
   cases I with
   | Ioo a b => exact le_of_lt (nonempty_Ioo_strictness h)
@@ -532,7 +532,7 @@ macro:max atomic("|" noWs) a:term noWs "|ₗ" : term => `(BoundedInterval.length
 structure Box (d:ℕ) where
   side : Fin d → BoundedInterval
 
-/-- Coerces a Box to its underlying set in d-dimensional Euclidean space. -/
+/-- Coerces a {name}`Box` to its underlying set in d-dimensional Euclidean space. -/
 @[coe]
 def Box.toSet {d:ℕ} (B: Box d) : Set (EuclideanSpace' d) :=
   {x | ∀ i, x i ∈ (B.side i : Set ℝ)}
@@ -541,7 +541,7 @@ def Box.toSet {d:ℕ} (B: Box d) : Set (EuclideanSpace' d) :=
 theorem Box.mem_toSet {d:ℕ} {B: Box d} {x : EuclideanSpace' d} :
     x ∈ B.toSet ↔ ∀ i, x i ∈ (B.side i : Set ℝ) := Iff.rfl
 
-/-- Enables coercion from Box d to Set (EuclideanSpace' d). -/
+/-- Enables coercion from {lean}`Box d` to {lean}`Set (EuclideanSpace' d)`. -/
 instance Box.inst_coeSet {d:ℕ} : Coe (Box d) (Set (EuclideanSpace' d)) where
   coe := toSet
 
@@ -550,18 +550,18 @@ instance Box.inst_coeSet {d:ℕ} : Coe (Box d) (Set (EuclideanSpace' d)) where
 abbrev BoundedInterval.toBox (I: BoundedInterval) : Box 1 where
   side := fun _ ↦ I
 
-/-- Enables coercion from BoundedInterval to Box 1. -/
+/-- Enables coercion from {name}`BoundedInterval` to {lean}`Box 1`. -/
 instance BoundedInterval.inst_coeBox : Coe (BoundedInterval) (Box 1) where
   coe := toBox
 
-/-- Coercing to Box 1 is injective: equal boxes implies equal intervals. -/
+/-- Coercing to {lean}`Box 1` is injective: equal boxes implies equal intervals. -/
 @[simp]
 theorem BoundedInterval.toBox_inj {I J: BoundedInterval} : (I:Box 1) = (J:Box 1) ↔ I = J := by
   refine' ⟨fun h => _, fun h => h ▸ rfl⟩
   have : (I:Box 1).side 0 = (J:Box 1).side 0 := by rw [h]
   exact this
 
-/-- A 1D box's set equals the image of the interval under the Real ≃ EuclideanSpace' 1 equivalence. -/
+/-- A 1D box's set equals the image of the interval under the {lean}`Real ≃ EuclideanSpace' 1` equivalence. -/
 @[simp]
 theorem BoundedInterval.coe_of_box (I:BoundedInterval) : (I:Box 1).toSet = Real.equiv_EuclideanSpace' '' I.toSet := by
   ext x; simp only [Box.mem_toSet, Set.mem_image]; constructor
@@ -601,7 +601,7 @@ lemma Box.volume_eq_zero_of_empty {d:ℕ} (B: Box d) (h: B.toSet = ∅) : |B|ᵥ
     | Ico a b, hi => simp [BoundedInterval.set_Ico] at hi; simp; exact le_of_not_gt (Set.Ico_eq_empty_iff.1 hi)
   simp [BoundedInterval.length, max_eq_right (sub_nonpos.2 h_le)]
 
-/-- A box with all degenerate sides [x, x] has volume 0 when d > 0 -/
+/-- A box with all degenerate sides \[x, x\] has volume 0 when d > 0 -/
 lemma Box.volume_singleton {d:ℕ} (hd : 0 < d) (x : EuclideanSpace' d) :
     |⟨fun i => BoundedInterval.Icc (x i) (x i)⟩|ᵥ = 0 := by
   unfold Box.volume BoundedInterval.length
@@ -627,7 +627,7 @@ lemma Box.side_nonempty_of_nonempty {d:ℕ} (B : Box d) (hB : B.toSet.Nonempty)
 theorem Box.volume_of_interval (I:BoundedInterval) : |(I:Box 1)|ᵥ = |I|ₗ := by
   simp [Box.volume]
 
-/-- Box.toSet is injective on non-empty boxes -/
+/-- {name}`Box.toSet` is injective on non-empty boxes -/
 lemma Box.toSet_injective_of_nonempty {d:ℕ} {B₁ B₂ : Box d}
     (h₁ : B₁.toSet.Nonempty) (h₂ : B₂.toSet.Nonempty) (h_eq : B₁.toSet = B₂.toSet) :
     B₁ = B₂ := by
@@ -792,8 +792,7 @@ theorem BoundedInterval.partition (S: Finset BoundedInterval) : ∃ T: Finset Bo
     refine' ⟨ Ioo (sorted ⟨ r-1, by omega ⟩) (sorted ⟨ r, hr ⟩), _ , _, _ ⟩
     . apply Set.Subset.trans _ I.Ioo_subset
       simp [hnI, hmI]
-      apply Set.Ioo_subset_Ioo <;> simp [Subtype.coe_le_coe] <;>
-        apply sorted.monotone <;> grind
+      apply Set.Ioo_subset_Ioo <;> simp [Subtype.coe_le_coe] <;> omega
     . simp [T]; refine' ⟨ r-1, by omega, _ ⟩
       simp [a, show r-1 < k by omega, show r < k by omega, show r-1+1=r by omega]
     simp
@@ -984,7 +983,7 @@ theorem IsElementary.measure_eq {d:ℕ} {E: Set (EuclideanSpace' d)} (hE: IsElem
   rw [←heq, ←hE.partition.choose_spec.2]
 
 /-- Exercise 1.1.2: give an alternate proof of this proposition by showing that
-the two partitions `T₁`, `T₂` admit a mutual refinement into boxes arising from
+the two partitions {lean}`T₁`, {lean}`T₂` admit a mutual refinement into boxes arising from
 taking Cartesian products of elements from finite collections of disjoint intervals. -/
 theorem Box.measure_uniq' {d:ℕ} {T₁ T₂: Finset (Box d)}
  (hT₁: (T₁ : Set (Box d)).PairwiseDisjoint Box.toSet)
@@ -993,7 +992,7 @@ theorem Box.measure_uniq' {d:ℕ} {T₁ T₂: Finset (Box d)}
  ∑ B ∈ T₁, |B|ᵥ = ∑ B ∈ T₂, |B|ᵥ := by
  sorry
 
-/-- Example: the measure of (1,2) ∪ [3,6] is 1 + 3 = 4. -/
+/-- Example: the measure of (1,2) ∪ \[3,6\] is 1 + 3 = 4. -/
 example :
   let E : Set (EuclideanSpace' 1) := Real.equiv_EuclideanSpace' '' ((Set.Ioo 1 2) ∪ (Set.Icc 3 6))
   ∃ hE : IsElementary E, hE.measure = 4 := by
@@ -1153,7 +1152,7 @@ lemma IsElementary.union'_empty_eq {d:ℕ} :
   simp
 
 open Classical in
-/-- Measure of a sum over `insert a S'` equals the measure of `a` plus the measure of the sum over `S'`. -/
+/-- Measure of a sum over {lean}`insert a S'` equals the measure of {lean}`a` plus the measure of the sum over {lean}`S'`. -/
 lemma IsElementary.sum_insert_split {d:ℕ} {a: Set (EuclideanSpace' d)} {S': Finset (Set (EuclideanSpace' d))}
     (ha : a ∉ S')
     (hE: ∀ E ∈ insert a S', IsElementary E) :
@@ -1464,7 +1463,7 @@ lemma Box.volume_of_translate {d:ℕ} (B: Box d) (x: EuclideanSpace' d) :
     ext i
     exact (hI' i).2
 
-/-- Translation is injective on sets: if S₁ + {x} = S₂ + {x}, then S₁ = S₂ -/
+/-- Translation is injective on sets: if S₁ + \{x\} = S₂ + \{x\}, then S₁ = S₂ -/
 lemma Set.translate_inj {d:ℕ} (x: EuclideanSpace' d) (S₁ S₂ : Set (EuclideanSpace' d))
   (h_eq : S₁ + {x} = S₂ + {x}) : S₁ = S₂ := by
   ext y
@@ -1482,7 +1481,7 @@ lemma Set.translate_inj {d:ℕ} (x: EuclideanSpace' d) (S₁ S₂ : Set (Euclide
     rw [Set.mem_singleton_iff.mp hb] at hab
     exact (add_right_cancel hab) ▸ ha
 
-/-- Elementary measure is translation-invariant: μ(E + {x}) = μ(E). -/
+/-- Elementary measure is translation-invariant: μ(E + \{x\}) = μ(E). -/
 lemma IsElementary.measure_of_translate {d:ℕ} {E: Set (EuclideanSpace' d)}
 (hE: IsElementary E) (x: EuclideanSpace' d):
   (hE.translate x).measure = hE.measure := by
@@ -1606,7 +1605,7 @@ theorem IsElementary.measure_uniq {d:ℕ} {m': (E: Set (EuclideanSpace' d)) →
   (htrans: ∀ E: Set (EuclideanSpace' d), ∀ (hE: IsElementary E) (x: EuclideanSpace' d), m' (E + {x}) (hE.translate x) = m' E hE) : ∃ c, c ≥ 0 ∧ ∀ E: Set (EuclideanSpace' d), ∀ hE: IsElementary E, m' E hE = c * hE.measure := by
     sorry
 
-/-- The d-dimensional unit cube (0,1]^d. -/
+/-- The d-dimensional unit cube (0,1\]^d. -/
 abbrev Box.unit_cube (d:ℕ) : Box d := { side := fun _ ↦ BoundedInterval.Ioc 0 1}
 
 /-- Any measure satisfying normalization m'(unit cube) = 1 must equal the standard elementary measure. -/
@@ -1629,7 +1628,7 @@ abbrev Box.prod {d₁ d₂:ℕ} (B₁: Box d₁) (B₂: Box d₂) : Box (d₁ +
 theorem IsElementary.prod {d₁ d₂:ℕ} {E₁: Set (EuclideanSpace' d₁)} {E₂: Set (EuclideanSpace' d₂)}
   (hE₁: IsElementary E₁) (hE₂: IsElementary E₂) : IsElementary (EuclideanSpace'.prod E₁ E₂) := by sorry
 
-/-- Measure is multiplicative on products: μ(E₁ × E₂) = μ(E₁) * μ(E₂). -/
+/-- Measure is multiplicative on products: μ(E₁ × E₂) = μ(E₁) \* μ(E₂). -/
 theorem IsElementary.measure_of_prod {d₁ d₂:ℕ} {E₁: Set (EuclideanSpace' d₁)} {E₂: Set (EuclideanSpace' d₂)}
   (hE₁: IsElementary E₁) (hE₂: IsElementary E₂)
   : (hE₁.prod hE₂).measure = hE₁.measure * hE₂.measure := by sorry
diff --git a/analysis/Analysis/MeasureTheory/Section_1_1_2.lean b/Analysis/MeasureTheory/Section_1_1_2.lean
similarity index 99%
rename from analysis/Analysis/MeasureTheory/Section_1_1_2.lean
rename to Analysis/MeasureTheory/Section_1_1_2.lean
index 574f0606..6a9ea60b 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_1_2.lean
+++ b/Analysis/MeasureTheory/Section_1_1_2.lean
@@ -8,8 +8,8 @@ A companion to Section 1.1.2 of the book "An introduction to Measure Theory".
 
 -/
 
-/-- Definition 1.1.4.  We intend these concepts to only be applied for bounded sets `E`, but
-it is convenient to permit `E` to be unbounded for the purposes of making the definitions.
+/-- Definition 1.1.4.  We intend these concepts to only be applied for bounded sets {lean}`E`, but
+it is convenient to permit {lean}`E` to be unbounded for the purposes of making the definitions.
 -/
 noncomputable abbrev Jordan_inner_measure {d:ℕ} (E: Set (EuclideanSpace' d)) : ℝ :=
   sSup { m:ℝ | ∃ (A: Set (EuclideanSpace' d)), ∃ hA: IsElementary A, A ⊆ E ∧ m = hA.measure }
@@ -776,7 +776,7 @@ theorem JordanMeasure.measure_eq {d:ℕ} {E: Set (EuclideanSpace' d)} (hE: Jorda
   Filter.atTop.Tendsto (fun N:ℕ ↦ (N:ℝ)^(-d:ℝ) * Nat.card ↥(E ∩ (Set.range (fun (n:Fin d → ℤ) ↦ .toLp 2 (fun i ↦ (N:ℝ)⁻¹*(n i))))))
   (nhds hE.measure) := by sorry
 
-/-- A dyadic box at scale 2^(-n) with multi-index i: the half-open cube [i/2^n, (i+1)/2^n). -/
+/-- A dyadic box at scale 2^(-n) with multi-index i: the half-open cube \[i/2^n, (i+1)/2^n). -/
 noncomputable abbrev Box.dyadic {d:ℕ} (n:ℤ) (i:Fin d → ℤ) : Box d where
   side j := BoundedInterval.Ico ((i j)/2^n) ((i j + 1)/2^n)
 
@@ -822,7 +822,7 @@ theorem JordanMeasure.measure_uniq' {d:ℕ} {m': (E: Set (EuclideanSpace' d)) 
 theorem JordanMeasurable.prod {d₁ d₂:ℕ} {E₁: Set (EuclideanSpace' d₁)} {E₂: Set (EuclideanSpace' d₂)}
   (hE₁: JordanMeasurable E₁) (hE₂: JordanMeasurable E₂) : JordanMeasurable (EuclideanSpace'.prod E₁ E₂) := by sorry
 
-/-- Jordan measure is multiplicative on products: μ(E₁ × E₂) = μ(E₁) * μ(E₂). -/
+/-- Jordan measure is multiplicative on products: μ(E₁ × E₂) = μ(E₁) \* μ(E₂). -/
 theorem JordanMeasurable.measure_of_prod {d₁ d₂:ℕ} {E₁: Set (EuclideanSpace' d₁)} {E₂: Set (EuclideanSpace' d₂)}
   (hE₁: JordanMeasurable E₁) (hE₂: JordanMeasurable E₂)
   : (hE₁.prod hE₂).measure = hE₁.measure * hE₂.measure := by sorry
diff --git a/analysis/Analysis/MeasureTheory/Section_1_1_3.lean b/Analysis/MeasureTheory/Section_1_1_3.lean
similarity index 97%
rename from analysis/Analysis/MeasureTheory/Section_1_1_3.lean
rename to Analysis/MeasureTheory/Section_1_1_3.lean
index e0c86b01..aee8c2e3 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_1_3.lean
+++ b/Analysis/MeasureTheory/Section_1_1_3.lean
@@ -9,7 +9,7 @@ A companion to Section 1.1.3 of the book "An introduction to Measure Theory".
 
 open BoundedInterval
 
-/-- Definition 1.1.5.  (Riemann integrability) The interval `I` should be closed, though we will not enforce this.  We also permit the length to be 0. We index the tags and deltas starting from 0 rather than 1
+/-- Definition 1.1.5.  (Riemann integrability) The interval {lean}`I` should be closed, though we will not enforce this.  We also permit the length to be 0. We index the tags and deltas starting from 0 rather than 1
 in the text as this is slightly more convenient in Lean. -/
 @[ext]
 structure TaggedPartition (I: BoundedInterval) (n:ℕ) where
@@ -31,14 +31,14 @@ noncomputable def TaggedPartition.norm {I: BoundedInterval} {n:ℕ} (P: TaggedPa
 def TaggedPartition.RiemannSum {I: BoundedInterval} {n:ℕ} (f: ℝ → ℝ) (P: TaggedPartition I n) : ℝ :=
   ∑ i, f (P.x_tag i) * P.delta i
 
-/-- `Sigma (TaggedPartition I)` is the type of all partitions of `I` with an unspecified number `n` of components.  Here we define what it means to converge to zero in this type. -/
+/-- {given (type := "ℕ") -show}`n` {lean}`Sigma (TaggedPartition I)` is the type of all partitions of {name}`I` with an unspecified number {name}`n` of components.  Here we define what it means to converge to zero in this type. -/
 -- A filter on Sigma (TaggedPartition I) converging to zero as the partition norm shrinks.
 noncomputable def TaggedPartition.nhds_zero (I: BoundedInterval) : Filter (Sigma (TaggedPartition I)) := Filter.comap (fun P ↦ P.snd.norm) (nhds 0)
 
 -- Riemann integrability: Riemann sums converge to R as the partition norm tends to zero.
 def riemann_integral_eq (f: ℝ → ℝ) (I: BoundedInterval) (R: ℝ) : Prop := (TaggedPartition.nhds_zero I).Tendsto (fun P ↦ TaggedPartition.RiemannSum f P.snd) (nhds R)
 
-/-- Construct a uniform partition of `[a,b]` into `n` equal pieces with left endpoint tags. -/
+/-- Construct a uniform partition of {lean}`[a,b]` into {lean}`n` equal pieces with left endpoint tags. -/
 noncomputable def TaggedPartition.uniform (I: BoundedInterval) (n: ℕ) (hn: n > 0) (_: I = Icc I.a I.b) (hab: I.a < I.b) : TaggedPartition I n where
   x := fun i => I.a + (I.b - I.a) * (i.val : ℝ) / n
   x_tag := fun i => I.a + (I.b - I.a) * (i.castSucc.val : ℝ) / n
@@ -122,7 +122,7 @@ lemma TaggedPartition.exists_norm_le (I: BoundedInterval) (hI: I = Icc I.a I.b)
       _ = δ := by field_simp
   linarith
 
-/-- The filter TaggedPartition.nhds_zero is non-trivial when the interval has positive length. -/
+/-- The filter {name}`TaggedPartition.nhds_zero` is non-trivial when the interval has positive length. -/
 instance TaggedPartition.nhds_zero_neBot (I: BoundedInterval) (hI: I = Icc I.a I.b) (hab: I.a < I.b) :
     Filter.NeBot (TaggedPartition.nhds_zero I) := by
   unfold TaggedPartition.nhds_zero
@@ -154,7 +154,7 @@ instance TaggedPartition.nhds_zero_neBot (I: BoundedInterval) (hI: I = Icc I.a I
       have h_le_sup : P.delta i0 ≤ iSup P.delta := le_ciSup h_bdd i0
       linarith
 
-/-- We enforce `I` to be closed and nonempty for the definition of Riemann integrability.
+/-- We enforce {lean}`I` to be closed and nonempty for the definition of Riemann integrability.
     The nonempty constraint ensures meaningful integration and excludes degenerate cases. -/
 -- A function is Riemann integrable on a closed interval if Riemann sums converge to some value.
 abbrev RiemannIntegrableOn (f: ℝ → ℝ) (I: BoundedInterval) : Prop :=
@@ -186,7 +186,7 @@ lemma riemann_sum_eq_zero_of_zero_length {f : ℝ → ℝ} {I : BoundedInterval}
     linarith
 
 /-- When an interval has zero length and Riemann sums converge to R, then R = 0.
-    This requires that the filter is non-trivial (NeBot), which holds when `I.a = I.b`. -/
+    This requires that the filter is non-trivial ({name}`Filter.NeBot`), which holds when {lean}`I.a = I.b`. -/
 lemma riemann_integral_eq_zero_of_zero_length {f : ℝ → ℝ} {I : BoundedInterval} {R : ℝ}
     (h_eq : I.a = I.b) (h_len : |I|ₗ = 0) (hR : riemann_integral_eq f I R) : R = 0 := by
   -- All Riemann sums are 0
@@ -235,7 +235,7 @@ lemma riemann_integral_eq_zero_of_zero_length {f : ℝ → ℝ} {I : BoundedInte
   -- By uniqueness of limits in Hausdorff spaces (ℝ is Hausdorff)
   exact tendsto_nhds_unique hR h_zero_to_zero
 
-/-- When a nonempty closed interval [a,b] has zero length, then a = b. -/
+/-- When a nonempty closed interval \[a,b\] has zero length, then a = b. -/
 lemma eq_of_length_zero_of_Icc {I : BoundedInterval}
     (hI : I = Icc I.a I.b) (h_len : |I|ₗ = 0) (h_nonempty : I.toSet.Nonempty) : I.a = I.b := by
   -- From zero length, we get I.b ≤ I.a
@@ -505,7 +505,7 @@ lemma TaggedPartition.uniform_delta {I: BoundedInterval} {n: ℕ} (hn: n > 0) (h
   field_simp
   push_cast; ring
 
-/-- For any x in [a,b], find the subinterval index containing x -/
+/-- For any x in \[a,b\], find the subinterval index containing x -/
 noncomputable def findSubintervalIndex (lo hi : ℝ) (n : ℕ) (hn : n > 0) (x : ℝ) (_hx : lo ≤ x ∧ x ≤ hi) : Fin n :=
   let k := min (Nat.floor ((x - lo) / ((hi - lo) / n))) (n - 1)
   ⟨k, by omega⟩
@@ -836,14 +836,14 @@ lemma integral_neg {I: BoundedInterval} (g: PiecewiseConstantFunction I) :
   ext J
   ring
 
-/-- Helper: Convert a PiecewiseConstantFunction to PiecewiseConstantOn and relate integrals -/
+/-- Helper: Convert a {name}`PiecewiseConstantFunction` to {name}`PiecewiseConstantOn` and relate integrals -/
 lemma to_PiecewiseConstantOn {I: BoundedInterval} (g: PiecewiseConstantFunction I) :
     ∃ (h: PiecewiseConstantOn g.f I), h.integral = g.integral := by
   have hg_agrees : g.agreesWith g.f := fun x hx => rfl
   use ⟨g, hg_agrees⟩
   exact PiecewiseConstantOn.integral_eq g.f ⟨g, hg_agrees⟩ g hg_agrees
 
-/-- Helper: Apply integral_mono between two PiecewiseConstantFunctions via PiecewiseConstantOn -/
+/-- Helper: Apply `PiecewiseConstantOn.integral_mono` between two {name}`PiecewiseConstantFunction`s via {name}`PiecewiseConstantOn` -/
 lemma integral_mono' {I: BoundedInterval}
     (g h: PiecewiseConstantFunction I) (h_pointwise: ∀ x ∈ I.toSet, g.f x ≤ h.f x) :
     g.integral ≤ h.integral := by
diff --git a/analysis/Analysis/MeasureTheory/Section_1_2_0.lean b/Analysis/MeasureTheory/Section_1_2_0.lean
similarity index 99%
rename from analysis/Analysis/MeasureTheory/Section_1_2_0.lean
rename to Analysis/MeasureTheory/Section_1_2_0.lean
index 24c930c5..f61b9aae 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_2_0.lean
+++ b/Analysis/MeasureTheory/Section_1_2_0.lean
@@ -905,7 +905,7 @@ lemma Lebesgue_outer_measure_eq_nat_indexed {d:ℕ} (hd: 0 < d) (E: Set (Euclide
 
 open Classical in
 /-- Helper lemma: If X is an infinite subset of ℕ, then the sum of its indicator function
-    (mapping elements of X to 1 and others to 0) diverges to ⊤ in EReal. -/
+    (mapping elements of X to 1 and others to 0) diverges to ⊤ in {name}`EReal`. -/
 lemma hasSum_indicator_top_of_infinite (X : Set ℕ) (hX : ¬X.Finite) :
     HasSum (fun n => if n ∈ X then (1 : EReal) else 0) ⊤ := by
   -- Strategy: Show that finite sums grow unboundedly.
@@ -1120,7 +1120,7 @@ lemma Lebesgue_outer_measure_of_dim_zero {E: Set (EuclideanSpace' 0)} :
       unfold BoundedInterval.length
       exact le_max_right _ _
 
-/-- Coercion ℝ → EReal preserves infimums for nonempty bounded-below sets -/
+/-- Coercion {lean}`ℝ → EReal` preserves infimums for nonempty bounded-below sets -/
 lemma EReal.sInf_image_coe {s : Set ℝ} (hs : s.Nonempty) (h_bdd : BddBelow s) :
     sInf ((fun x : ℝ => (x : EReal)) '' s) = ↑(sInf s) := by
   -- Strategy: Show both ≤ directions using sInf properties
diff --git a/analysis/Analysis/MeasureTheory/Section_1_2_1.lean b/Analysis/MeasureTheory/Section_1_2_1.lean
similarity index 97%
rename from analysis/Analysis/MeasureTheory/Section_1_2_1.lean
rename to Analysis/MeasureTheory/Section_1_2_1.lean
index d4761fa5..5a0bb7bc 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_2_1.lean
+++ b/Analysis/MeasureTheory/Section_1_2_1.lean
@@ -11,12 +11,12 @@ A companion to (the introduction to) Section 1.2.1 of the book "An introduction
 
 open BoundedInterval
 
-/-- Express `Box.toSet` as a preimage of a pi set under the PiLp homeomorphism. -/
+/-- Express {name}`Box.toSet` as a preimage of a pi set under the {name}`PiLp` homeomorphism. -/
 lemma Box.toSet_eq_ofLp_preimage {d : ℕ} (B : Box d) :
     B.toSet = (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)) ⁻¹' Set.univ.pi (fun i => (B.side i).toSet) := by
   ext x; simp only [Box.mem_toSet, Set.mem_preimage, Set.mem_pi, Set.mem_univ, true_implies]; rfl
 
-/-- The interior of `Box.toSet` expressed as a preimage. -/
+/-- The interior of {name}`Box.toSet` expressed as a preimage. -/
 lemma Box.interior_toSet {d : ℕ} (B : Box d) :
     interior B.toSet = (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)) ⁻¹'
       Set.univ.pi (fun i => interior (B.side i).toSet) := by
@@ -24,7 +24,7 @@ lemma Box.interior_toSet {d : ℕ} (B : Box d) :
     ← (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)).preimage_interior,
     interior_pi_set Set.finite_univ]
 
-/-- The closure of `Box.toSet` expressed as a preimage. -/
+/-- The closure of {name}`Box.toSet` expressed as a preimage. -/
 lemma Box.closure_toSet {d : ℕ} (B : Box d) :
     closure B.toSet = (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)) ⁻¹'
       Set.univ.pi (fun i => closure (B.side i).toSet) := by
@@ -32,14 +32,14 @@ lemma Box.closure_toSet {d : ℕ} (B : Box d) :
     ← (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)).preimage_closure,
     closure_pi_set]
 
-/-- The frontier of `Box.toSet` expressed via the PiLp homeomorphism. -/
+/-- The frontier of {name}`Box.toSet` expressed via the {name}`PiLp` homeomorphism. -/
 lemma Box.frontier_toSet {d : ℕ} (B : Box d) :
     frontier B.toSet = (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)) ⁻¹'
       frontier (Set.univ.pi (fun i => (B.side i).toSet)) := by
   rw [Box.toSet_eq_ofLp_preimage,
     ← (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)).preimage_frontier]
 
-/-- A box with Icc sides is closed. -/
+/-- A box with {name}`BoundedInterval.Icc` sides is closed. -/
 lemma Box.isClosed_toSet_of_Icc {d : ℕ} (B : Box d)
     (h : ∀ i, ∃ a b, B.side i = BoundedInterval.Icc a b) : IsClosed B.toSet := by
   rw [Box.toSet_eq_ofLp_preimage]
@@ -152,7 +152,7 @@ noncomputable def set_dist {X:Type*} [PseudoMetricSpace X] (A B: Set X) : ℝ :=
 -- ========================================================================
 
 namespace BoundedInterval
-/-- Extract the left and right endpoints of a BoundedInterval.
+/-- Extract the left and right endpoints of a {name}`BoundedInterval`.
     Returns (a, b) where a is the left endpoint and b is the right endpoint. -/
 def endpoints (I : BoundedInterval) : ℝ × ℝ :=
   match I with
@@ -161,13 +161,13 @@ def endpoints (I : BoundedInterval) : ℝ × ℝ :=
   | Ioc a b => (a, b)
   | Ico a b => (a, b)
 
-/-- Compute the midpoint of a BoundedInterval. -/
+/-- Compute the midpoint of a {name}`BoundedInterval`. -/
 noncomputable def midpoint (I : BoundedInterval) : ℝ :=
   let (a, b) := I.endpoints
   (a + b) / 2
 
-/-- Bisect a BoundedInterval into left and right halves using closed intervals.
-    Left half: [a, m], Right half: [m, b], where m is the midpoint.
+/-- Bisect a {name}`BoundedInterval` into left and right halves using closed intervals.
+    Left half: \[a, m\], Right half: \[m, b\], where m is the midpoint.
     Using closed intervals ensures coverage (union equals original) while
     maintaining measure-theoretic properties (overlap has measure zero). -/
 noncomputable def bisect (I : BoundedInterval) : BoundedInterval × BoundedInterval :=
@@ -259,7 +259,7 @@ lemma midpoint_eq_a_add_half_length (I : BoundedInterval) (h : I.a ≤ I.b) :
     simp [max_eq_left (sub_nonneg.mpr h)]; ring
 
 
-/-- The midpoint is in the first half of bisection (as the right endpoint of Icc) -/
+/-- The midpoint is in the first half of bisection (as the right endpoint of {name}`BoundedInterval.Icc`) -/
 lemma midpoint_mem_bisect_fst (I : BoundedInterval) (h : I.toSet.Nonempty) :
     I.midpoint ∈ (I.bisect.fst).toSet := by
   obtain ⟨x, hx⟩ := h
@@ -278,7 +278,7 @@ lemma midpoint_mem_bisect_fst (I : BoundedInterval) (h : I.toSet.Nonempty) :
     simp only [Set.mem_Ico] at hx
     simp only [Set.mem_Icc]; exact ⟨by linarith, by linarith⟩
 
-/-- The midpoint is in the second half of bisection (as the left endpoint of Icc) -/
+/-- The midpoint is in the second half of bisection (as the left endpoint of {name}`BoundedInterval.Icc`) -/
 lemma midpoint_mem_bisect_snd (I : BoundedInterval) (h : I.toSet.Nonempty) :
     I.midpoint ∈ (I.bisect.snd).toSet := by
   obtain ⟨x, hx⟩ := h
@@ -555,7 +555,7 @@ lemma dist_le_diameter {d:ℕ} (B: Box d) {x y: EuclideanSpace' d}
 
 /-- For any nonempty interval and target value less than the length,
     we can find two points in the interval with separation exceeding the target.
-    This is the key density fact: achievable differences are dense in [0, length]. -/
+    This is the key density fact: achievable differences are dense in \[0, length\]. -/
 lemma BoundedInterval.exists_points_with_diff {I : BoundedInterval}
     (h_nonempty : I.toSet.Nonempty) {t : ℝ} (ht_nonneg : 0 ≤ t) (ht : t < |I|ₗ) :
     ∃ x ∈ I.toSet, ∃ y ∈ I.toSet, t < |x - y| := by
@@ -846,7 +846,7 @@ lemma diameter_ge_dist_of_intersects {d:ℕ} (B: Box d) (E F : Set (EuclideanSpa
     _ = √(∑ i, (x i - y i)^2) := h_eq
     _ ≤ B.diameter := h_le_diam
 
-/-- If B.diameter < set_dist E F, then B cannot intersect both E and F.
+/-- If B.diameter < set\_dist E F, then B cannot intersect both E and F.
     This is the core geometric fact needed for finite additivity of separated sets. -/
 lemma not_intersects_both_of_diameter_lt {d:ℕ} (B: Box d) (E F : Set (EuclideanSpace' d))
     (h : B.diameter < set_dist E F) :
@@ -858,12 +858,12 @@ lemma not_intersects_both_of_diameter_lt {d:ℕ} (B: Box d) (E F : Set (Euclidea
   linarith
 
 open Classical in
-/-- Decidable equality for boxes, needed for Finset operations -/
+/-- Decidable equality for boxes, needed for {name}`Finset` operations -/
 noncomputable instance {d:ℕ} : DecidableEq (Box d) := instDecidableEqOfLawfulBEq
 
 /-- Subdivide a box by bisecting each coordinate axis, producing 2^d sub-boxes.
     Each sub-box is formed by taking one half-interval from each coordinate.
-    We use Finset.univ (all possible d-bit patterns) to enumerate all 2^d combinations. -/
+    We use {name}`Finset.univ` (all possible d-bit patterns) to enumerate all 2^d combinations. -/
 noncomputable def subdivide {d:ℕ} (B: Box d) : Finset (Box d) :=
   -- For each choice ∈ Fin d → Bool (which half to take for each coordinate),
   -- construct a sub-box by taking the left half (if false) or right half (if true)
@@ -996,7 +996,8 @@ lemma volume_subdivide {d:ℕ} (B: Box d) :
 /-- Each sub-box of a subdivision has diameter at most the original diameter divided by √2.
     This follows because each side is halved, reducing the diagonal by a factor related to √2.
     Note: The hypothesis that B is nonempty is necessary because bisection always creates closed
-    intervals, which can turn degenerate open intervals (Ioo a a) into nonempty singletons. -/
+    intervals, which can turn degenerate open intervals ({given -show}`a` {lean}`Ioo a a`) into
+    nonempty singletons. -/
 lemma subdivide_diameter_bound {d:ℕ} (B: Box d) (hB : B.toSet.Nonempty) :
     ∀ B' ∈ B.subdivide, B'.diameter ≤ B.diameter / Real.sqrt 2 := by
   intro B' hB'
@@ -1048,8 +1049,8 @@ lemma subdivide_diameter_bound {d:ℕ} (B: Box d) (hB : B.toSet.Nonempty) :
   rw [h_sum_eq, Real.sqrt_div (Finset.sum_nonneg (fun i _ => sq_nonneg _))]
   norm_num
 
-/-- Subdivide a box k times, producing a Finset of boxes.
-    After k iterations, each original box becomes up to 2^(d*k) sub-boxes. -/
+/-- Subdivide a box k times, producing a {name}`Finset` of boxes.
+    After k iterations, each original box becomes up to 2^(d\*k) sub-boxes. -/
 noncomputable def subdivide_iter {d:ℕ} (B: Box d) : ℕ → Finset (Box d)
   | 0 => {B}
   | k+1 => (subdivide_iter B k).biUnion Box.subdivide
@@ -1059,7 +1060,7 @@ lemma subdivide_iter_zero {d:ℕ} (B: Box d) : subdivide_iter B 0 = {B} := rfl
 lemma subdivide_iter_succ {d:ℕ} (B: Box d) (k: ℕ) :
     subdivide_iter B (k+1) = (subdivide_iter B k).biUnion Box.subdivide := rfl
 
-/-- All sides in subdivide (single level) are Icc intervals -/
+/-- All sides in {name}`Box.subdivide` (single level) are {name}`BoundedInterval.Icc` intervals -/
 lemma subdivide_side_is_Icc {d:ℕ} (B: Box d) (B' : Box d) (hB' : B' ∈ B.subdivide) (i : Fin d) :
     ∃ a b, B'.side i = Icc a b := by
   simp only [subdivide, Finset.mem_image, Finset.mem_univ, true_and] at hB'
@@ -1075,7 +1076,7 @@ lemma subdivide_side_is_Icc {d:ℕ} (B: Box d) (B' : Box d) (hB' : B' ∈ B.subd
     unfold BoundedInterval.bisect BoundedInterval.endpoints BoundedInterval.midpoint
     cases B.side i <;> exact ⟨_, _, rfl⟩
 
-/-- All sides in subdivide_iter for k ≥ 1 are Icc intervals -/
+/-- All sides in {name}`Box.subdivide_iter` for k ≥ 1 are {name}`BoundedInterval.Icc` intervals -/
 lemma subdivide_iter_side_is_Icc {d:ℕ} (B: Box d) (k : ℕ) (B' : Box d)
     (hB' : B' ∈ subdivide_iter B (k+1)) (i : Fin d) :
     ∃ a b, B'.side i = Icc a b := by
@@ -1089,7 +1090,7 @@ lemma subdivide_iter_side_is_Icc {d:ℕ} (B: Box d) (k : ℕ) (B' : Box d)
     obtain ⟨B'', hB'', hB'_sub⟩ := hB'
     exact subdivide_side_is_Icc B'' B' hB'_sub i
 
-/-- All boxes in subdivide_iter have the same side lengths at each coordinate -/
+/-- All boxes in {name}`Box.subdivide_iter` have the same side lengths at each coordinate -/
 lemma subdivide_iter_side_length {d:ℕ} (B : Box d) (k : ℕ) (B' : Box d)
     (hB' : B' ∈ subdivide_iter B k) (i : Fin d) :
     |B'.side i|ₗ = |B.side i|ₗ / 2^k := by
@@ -1139,7 +1140,7 @@ lemma subdivide_iter_nonempty {d:ℕ} (B: Box d) (hB: B.toSet.Nonempty) (k: ℕ)
     obtain ⟨B'', hB''_mem, hB'_sub⟩ := hB'
     exact subdivide_one_step_nonempty B'' (ih B'' hB''_mem) B' hB'_sub
 
-/-- Grid alignment: sides in subdivide_iter start at grid positions.
+/-- Grid alignment: sides in {name}`Box.subdivide_iter` start at grid positions.
     Requires nonempty box to ensure sides have a ≤ b (backwards intervals break the formula). -/
 lemma subdivide_iter_side_grid {d:ℕ} (B : Box d) (hB : B.toSet.Nonempty) (k : ℕ) (B' : Box d)
     (hB' : B' ∈ subdivide_iter B k) (i : Fin d) :
@@ -1421,14 +1422,14 @@ lemma diameter_subdivide_iter {d:ℕ} (B: Box d) (hB: B.toSet.Nonempty) (k: ℕ)
 
 /-- Number of subdivisions needed to get diameter below threshold r.
     Each subdivision reduces diameter by factor of √2, so after k iterations:
-    diameter ≤ original_diameter / (√2)^k
+    diameter ≤ original\_diameter / (√2)^k
     We need (√2)^k > diameter/r, i.e., k > log(diameter/r) / log(√2) = 2·log₂(diameter/r). -/
 noncomputable def iter_count {d:ℕ} (B: Box d) (r: ℝ) : ℕ :=
   if B.diameter ≤ 0 then 0
   else if B.diameter < r then 0
   else Nat.ceil (2 * Real.log (B.diameter / r) / Real.log 2) + 1
 
-/-- After iter_count subdivisions, all sub-boxes have diameter < r -/
+/-- After iter\_count subdivisions, all sub-boxes have diameter < r -/
 lemma diameter_lt_of_iter_count {d:ℕ} (B: Box d) (hB: B.toSet.Nonempty) (r: ℝ) (hr: 0 < r) :
     ∀ B' ∈ subdivide_iter B (B.iter_count r), B'.diameter < r := by
   intro B' hB'
@@ -1508,7 +1509,7 @@ lemma diameter_lt_of_iter_count {d:ℕ} (B: Box d) (hB: B.toSet.Nonempty) (r: 
               _ = r * (2 : ℝ) ^ (((B.iter_count r) : ℝ) / 2) := by ring
 
 /-- Subdivided boxes cover the original box: any point in B.toSet is contained in
-    some box in subdivide_iter B k. -/
+    some box in subdivide\_iter B k. -/
 lemma subdivide_iter_covers {d:ℕ} (B : Box d) (k : ℕ) (x : EuclideanSpace' d)
     (hx : x ∈ B.toSet) : ∃ B' ∈ subdivide_iter B k, x ∈ B'.toSet := by
   induction k with
@@ -1552,7 +1553,7 @@ lemma volume_nonneg {d : ℕ} (B : Box d) : 0 ≤ B.volume := by
   unfold BoundedInterval.length
   exact le_max_right _ _
 
-/-- Closed boxes (all sides are Icc) in Euclidean space are compact sets. -/
+/-- Closed boxes (all sides are {name}`BoundedInterval.Icc`) in Euclidean space are compact sets. -/
 lemma isCompact {d : ℕ} (B : Box d) (h_closed : ∀ i, ∃ a b, B.side i = BoundedInterval.Icc a b) :
     IsCompact B.toSet := by
   -- Use Tychonoff: product of compact sets is compact
@@ -1585,15 +1586,15 @@ lemma le_of_nat_cover {d:ℕ} (hd: 0 < d) (E: Set (EuclideanSpace' d))
   · -- S is in the set of covers
     exact ⟨S, hcover, rfl⟩
 
-/-- Upper bound from finset-indexed cover: if a set is covered by ⋃ n, ⋃ B ∈ I n, B.toSet
-    where each I n is a finite set of boxes, then the outer measure is bounded by the
+/-- Upper bound from finset-indexed cover: if a set is covered by {lean}`⋃ n, ⋃ B ∈ I n, B.toSet`
+    where each {given -show}`n` {lean}`I n` is a finite set of boxes, then the outer measure is bounded by the
     sum of volumes.
 
     Proof strategy:
-    1. The sigma type (n : ℕ) × ↑(I n) is countable (and hence encodable)
-    2. Use Encodable instance to define S : ℕ → Box d via decoding
+    1. The sigma type {lean}`(n : ℕ) × ↑(I n)` is countable (and hence {name}`Encodable`)
+    2. Use {name}`Encodable` instance to define {lit}`S` of type {lean}`ℕ → Box d` via decoding
     3. Pad with zero-volume box for invalid decodings
-    4. Apply le_of_nat_cover and bound the enumerated sum -/
+    4. Apply {name}`Lebesgue_outer_measure.le_of_nat_cover` and bound the enumerated sum -/
 lemma le_of_finset_cover {d:ℕ} (hd: 0 < d) (E: Set (EuclideanSpace' d))
     (I : ℕ → Finset (Box d)) (hcover : E ⊆ ⋃ n, ⋃ B ∈ I n, B.toSet) :
     Lebesgue_outer_measure E ≤ ∑' n, (∑ B ∈ I n, B.volume).toEReal := by
@@ -1903,18 +1904,18 @@ end Lebesgue_outer_measure
 -- ========================================================================
 
 /-- Lemma 1.2.5 (Finite additivity for separated sets).
-    If E and F are separated (dist(E,F) > 0), then m*(E ∪ F) = m*(E) + m*(F).
+    If E and F are separated (dist(E,F) > 0), then m\*(E ∪ F) = m\*(E) + m\*(F).
 
     Proof strategy (from textbook):
     1. Direction ≤: Use subadditivity
-    2. Direction ≥: Show m*(E ∪ F) ≥ m*(E) + m*(F)
-       - If m*(E ∪ F) = ⊤, trivial
-       - If m*(E ∪ F) < ⊤:
-         * Get epsilon-close cover of E ∪ F
-         * Refine cover so all boxes have diameter < dist(E,F)
-         * Partition boxes into E-intersecting and F-intersecting (disjoint by geometric separation)
-         * Sum volumes separately: m*(E) + m*(F) ≤ sum of refined cover ≤ m*(E ∪ F) + ε
-         * Take ε → 0 to conclude
+    2. Direction ≥: Show m\*(E ∪ F) ≥ m\*(E) + m\*(F)
+       - If m\*(E ∪ F) = ⊤, trivial
+       - If m\*(E ∪ F) < ⊤:
+         \* Get epsilon-close cover of E ∪ F
+         \* Refine cover so all boxes have diameter < dist(E,F)
+         \* Partition boxes into E-intersecting and F-intersecting (disjoint by geometric separation)
+         \* Sum volumes separately: m\*(E) + m\*(F) ≤ sum of refined cover ≤ m\*(E ∪ F) + ε
+         \* Take ε → 0 to conclude
 -/
 theorem Lebesgue_outer_measure.union_of_separated {d:ℕ} (hd: 0 < d) {E F : Set (EuclideanSpace' d)}
     (hsep: set_dist E F > 0) :
@@ -2171,7 +2172,7 @@ theorem dist_of_disj_compact_pos {d:ℕ} (E F: Set (EuclideanSpace' d)) (hE: IsC
 -- Start of Helper lemmas for Lemma 1.2.6
 -- ========================================================================
 
-/-- Sum of geometric series δ/2^{n+2} equals δ/2 -/
+/-- Sum of geometric series δ/2^\{n+2\} equals δ/2 -/
 lemma tsum_geometric_inflate {δ : ℝ} (_hδ : 0 < δ) :
     ∑' n : ℕ, δ / 2^(n+2) = δ / 2 := by
   -- ∑ δ/2^{n+2} = δ/4 * ∑ (1/2)^n = δ/4 * 2 = δ/2
@@ -2184,7 +2185,7 @@ lemma tsum_geometric_inflate {δ : ℝ} (_hδ : 0 < δ) :
     rw [← mul_pow]; norm_num
   rw [h_eq, tsum_mul_left, tsum_geometric_of_lt_one (by norm_num : (0:ℝ) ≤ 1/2) (by norm_num : (1:ℝ)/2 < 1)]
   ring
-/-- When P_nonempty ⊆ P, the loss from scaling is bounded by δ/4. -/
+/-- When P\_nonempty ⊆ P, the loss from scaling is bounded by δ/4. -/
 lemma card_ratio_bound {P_nonempty P : Finset α} (hP_nonempty_sub : P_nonempty ⊆ P)
     {δ : ℝ} (hδ_pos : 0 < δ) (hcard_pos : 0 < P.card) :
     P_nonempty.card * (δ / (4 * P.card)) ≤ δ / 4 := by
@@ -2197,7 +2198,7 @@ lemma card_ratio_bound {P_nonempty P : Finset α} (hP_nonempty_sub : P_nonempty
     _ = δ / 4 := by field_simp [hP_card_pos.ne.symm]
 
 /-- Sum bound from partition filter: if volumes B' satisfy B.vol ≤ B'.vol + ε,
-    then summing over P_nonempty gives total bound with card * ε term. -/
+    then summing over P\_nonempty gives total bound with card \* ε term. -/
 lemma partition_volume_bound {d : ℕ} {P : Finset (Box d)}
     {P_nonempty : Finset (Box d)} (_hP_nonempty_sub : P_nonempty ⊆ P)
     {B' : (B : Box d) → B ∈ P_nonempty → Box d}
@@ -2249,7 +2250,7 @@ lemma injective_of_shrunk_nonempty {d : ℕ} {P : Finset (Box d)}
   rw [h_inter_empty] at h_in_inter
   exact Set.not_nonempty_empty (h_B'₁_nonempty.mono h_in_inter)
 
-/-- Every bounded interval (Ioo, Icc, Ioc, Ico) is a bounded set -/
+/-- Every bounded interval ({name}`BoundedInterval.Ioo`, {name}`BoundedInterval.Icc`, {name}`BoundedInterval.Ioc`, {name}`BoundedInterval.Ico`) is a bounded set -/
 lemma BoundedInterval.isBounded (I: BoundedInterval) : Bornology.IsBounded I.toSet := by
   cases I with
   | Ioo a b => simp only [toSet]; exact Metric.isBounded_Ioo a b
@@ -2577,7 +2578,7 @@ lemma measure_of_empty_eq {d : ℕ} {E : Set (EuclideanSpace' d)}
   rw [this, IsElementary.measure_of_empty]
 
 
-/-- Finite indexed union of boxes is elementary (uses IsElementary.union' which takes a finset of sets) -/
+/-- Finite indexed union of boxes is elementary (uses {name}`IsElementary.union'` which takes a finset of sets) -/
 lemma iUnion_boxes {d : ℕ} {ι : Type*} [Fintype ι] (B : ι → Box d) :
     IsElementary (⋃ i, (B i).toSet) := by
   classical
@@ -3005,7 +3006,7 @@ lemma measure_le_cover_sum {d : ℕ} (_hd : 0 < d) {E : Set (EuclideanSpace' d)}
 
 /-- Direction 1: Elementary measure is a lower bound for outer measure
     (Partition gives a finite cover, outer measure is infimum over covers)
-    Uses measure_le_cover_sum for the core Heine-Borel argument. -/
+    Uses measure\_le\_cover\_sum for the core Heine-Borel argument. -/
 lemma measure_le_outer_measure {d:ℕ} (hd: 0 < d) {E: Set (EuclideanSpace' d)}
     (hE: IsElementary E) : (hE.measure : EReal) ≤ Lebesgue_outer_measure E := by
   -- Use ε-argument: show ∀ ε > 0, hE.measure ≤ m*(E) + ε
@@ -3034,7 +3035,7 @@ lemma measure_le_outer_measure {d:ℕ} (hd: 0 < d) {E: Set (EuclideanSpace' d)}
         exact_mod_cast (by linarith : ε / 2 ≤ ε)
 
 /-- Direction 2: Outer measure is bounded by elementary measure
-    (Uses: m*(E) ≤ J*(E) for bounded E, and J*(E) ≤ hE.measure for elementary E) -/
+    (Uses: m\*(E) ≤ J\*(E) for bounded E, and J\*(E) ≤ hE.measure for elementary E) -/
 lemma outer_measure_le_measure {d:ℕ} (_hd: 0 < d) {E: Set (EuclideanSpace' d)}
     (hE: IsElementary E) : Lebesgue_outer_measure E ≤ (hE.measure : EReal) := by
   -- Step 1: Lebesgue outer measure ≤ Jordan outer measure (for bounded sets)
@@ -3162,14 +3163,14 @@ example {d:ℕ} {hd: 0 < d} : ∃ (S:Type) (E: S → Set (EuclideanSpace' d)), 
 --  Start of Helpers for remark 1.2.8 -/
 -- ========================================================================
 
-/-- The distance on EuclideanSpace' 1 equals the distance in ℝ via equiv_Real -/
+/-- The distance on {lean}`EuclideanSpace' 1` equals the distance in ℝ via {name}`EuclideanSpace'.equiv_Real` -/
 lemma EuclideanSpace'_dist_eq_Real_dist (x y : EuclideanSpace' 1) :
     dist x y = dist (EuclideanSpace'.equiv_Real x) (EuclideanSpace'.equiv_Real y) := by
   rw [EuclideanSpace.dist_eq, Real.dist_eq]
   simp only [Fin.zero_eta, Real.sqrt_sq_eq_abs, EuclideanSpace'.equiv_Real, Equiv.coe_fn_mk,
     Fin.sum_univ_one, Real.dist_eq, abs_abs]
 
-/-- Preimage of closed interval [a,b] under equiv_Real equals the corresponding 1D box -/
+/-- Preimage of closed interval \[a,b\] under {name}`EuclideanSpace'.equiv_Real` equals the corresponding 1D box -/
 lemma preimage_Icc_eq_box (a b : ℝ) :
     EuclideanSpace'.equiv_Real ⁻¹' Set.Icc a b = (BoundedInterval.Icc a b).toBox.toSet := by
   rw [BoundedInterval.coe_of_box]
@@ -3183,7 +3184,7 @@ lemma preimage_Icc_eq_box (a b : ℝ) :
     simp [Real.equiv_EuclideanSpace', EuclideanSpace'.equiv_Real] at hy ⊢
     exact hy
 
-/-- Geometric series: ∑ ε/2^{n+1} = ε -/
+/-- Geometric series: ∑ ε/2^\{n+1\} = ε -/
 lemma tsum_geometric_eps (ε : ℝ) (_hε : 0 < ε) : ∑' n : ℕ, ε / 2^(n+1) = ε := by
   have h_eq : (fun n => ε / 2^(n+1)) = (fun n => ε / 2 * (1/2 : ℝ)^n) := by
     ext n
@@ -3214,7 +3215,7 @@ lemma tsum_interval_summable (ε : ℝ) : Summable (fun n => 2 * ε / 2^(n+1) :
 
 namespace Lebesgue_outer_measure
 
-/-- Lebesgue outer measure of a closed interval [a,b] equals b - a -/
+/-- Lebesgue outer measure of a closed interval \[a,b\] equals b - a -/
 lemma of_Icc (a b : ℝ) (hab : a ≤ b) :
     Lebesgue_outer_measure (EuclideanSpace'.equiv_Real ⁻¹' Set.Icc a b) = ((b - a : ℝ) : EReal) := by
   -- [a,b] is a single box in 1D, hence elementary with measure b - a
@@ -3270,7 +3271,7 @@ lemma Jordan_outer_measure_mono {E F : Set (EuclideanSpace' 1)}
 
 namespace Remark_1_2_8
 
-/-- Rationals in [0,1] form a nonempty countable set. -/
+/-- Rationals in \[0,1\] form a nonempty countable set. -/
 lemma rationals_unit_interval_nonempty : (Set.Icc (0:ℝ) 1 ∩ Set.range (fun q:ℚ ↦ (q:ℝ))).Nonempty := by
   use 0
   constructor
@@ -3280,14 +3281,14 @@ lemma rationals_unit_interval_nonempty : (Set.Icc (0:ℝ) 1 ∩ Set.range (fun q
 lemma rationals_unit_interval_countable : (Set.Icc (0:ℝ) 1 ∩ Set.range (fun q:ℚ ↦ (q:ℝ))).Countable :=
   Set.Countable.mono Set.inter_subset_right (Set.countable_range _)
 
-/-- An enumeration function of rationals in [0,1] -/
+/-- An enumeration function of rationals in \[0,1\] -/
 noncomputable def q_enum : ℕ → { x : ℝ // x ∈ Set.Icc (0:ℝ) 1 ∩ Set.range (fun q:ℚ ↦ (q:ℝ)) } :=
   (rationals_unit_interval_countable.exists_surjective rationals_unit_interval_nonempty).choose
 
 lemma q_enum_surj : Function.Surjective q_enum :=
   (rationals_unit_interval_countable.exists_surjective rationals_unit_interval_nonempty).choose_spec
 
-/-- An enumeration of rationals in [0,1] as real numbers -/
+/-- An enumeration of rationals in \[0,1\] as real numbers -/
 noncomputable def q (n : ℕ) : ℝ := (q_enum n).val
 
 lemma q_mem (n : ℕ) : q n ∈ Set.Icc (0:ℝ) 1 ∩ Set.range (fun r:ℚ ↦ (r:ℝ)) :=
@@ -3302,22 +3303,22 @@ lemma q_surj : ∀ x ∈ Set.Icc (0:ℝ) 1 ∩ Set.range (fun r:ℚ ↦ (r:ℝ))
   unfold q
   rw [hn]
 
-/-- The counterexample set U: union of open intervals around rationals in [0,1].
-    U(ε) = ⋃_{n:ℕ} (q_n - ε/2^{n+1}, q_n + ε/2^{n+1}) -/
+/-- The counterexample set U: union of open intervals around rationals in \[0,1\].
+    U(ε) = ⋃\_\{n:ℕ\} (q\_n - ε/2^\{n+1\}, q\_n + ε/2^\{n+1\}) -/
 noncomputable def U_real (ε : ℝ) : Set ℝ :=
   ⋃ n : ℕ, Set.Ioo (q n - ε / 2^(n+1)) (q n + ε / 2^(n+1))
 
-/-- The set U lifted to EuclideanSpace' 1 -/
+/-- The set U lifted to {lean}`EuclideanSpace' 1` -/
 noncomputable def U (ε : ℝ) : Set (EuclideanSpace' 1) :=
   EuclideanSpace'.equiv_Real ⁻¹' (U_real ε)
 
-/-- U_real is open (union of open intervals) -/
+/-- U\_real is open (union of open intervals) -/
 lemma U_real_isOpen (ε : ℝ) : IsOpen (U_real ε) := by
   apply isOpen_iUnion
   intro _
   exact isOpen_Ioo
 
-/-- U is open in EuclideanSpace' 1 -/
+/-- U is open in {lean}`EuclideanSpace' 1` -/
 lemma U_isOpen (ε : ℝ) : IsOpen (U ε) := by
   apply IsOpen.preimage _ (U_real_isOpen ε)
   exact PiLp.continuous_apply 2 (fun _ : Fin 1 => ℝ) _
@@ -3330,7 +3331,7 @@ noncomputable def radius (ε : ℝ) (n : ℕ) : ℝ := ε / 2^(n+1)
   -- apply div_pos hε
   -- exact pow_pos (by norm_num : (0:ℝ) < 2) (n+1)
 
-/-- U_real is contained in (-ε, 1+ε) -/
+/-- U\_real is contained in (-ε, 1+ε) -/
 lemma U_real_subset (ε : ℝ) (hε : 0 < ε) : U_real ε ⊆ Set.Ioo (-ε) (1 + ε) := by
   intro x hx
   simp only [U_real, Set.mem_iUnion] at hx
@@ -3385,7 +3386,7 @@ lemma component_lebesgue_le (ε : ℝ) (hε : 0 < ε) (n : ℕ) :
   simp only [h_length] at h1
   exact h1
 
-/-- Closure of U_real contains [0,1] (density of rationals) -/
+/-- Closure of U\_real contains \[0,1\] (density of rationals) -/
 lemma U_real_closure_contains_unit_interval (ε : ℝ) (hε : 0 < ε) :
     Set.Icc 0 1 ⊆ closure (U_real ε) := by
   intro x hx
@@ -3438,13 +3439,13 @@ lemma U_real_closure_contains_unit_interval (ε : ℝ) (hε : 0 < ε) :
   have hqn_in_t : q n ∈ t := hδ_sub hqn_in_ball
   exact ⟨q n, hqn_in_t, hqn_in_U⟩
 
-/-- Unit interval [0,1] as a BoundedInterval -/
+/-- Unit interval \[0,1\] as a {name}`BoundedInterval` -/
 abbrev unit_interval : BoundedInterval := BoundedInterval.Icc 0 1
 
-/-- Unit box in 1D: [0,1] lifted to Box 1 -/
+/-- Unit box in 1D: \[0,1\] lifted to {lean}`Box 1` -/
 abbrev unit_box_1D : Box 1 := unit_interval.toBox
 
-/-- Unit interval as the preimage of [0,1] equals unit box -/
+/-- Unit interval as the preimage of \[0,1\] equals unit box -/
 lemma unit_interval_eq_box : EuclideanSpace'.equiv_Real ⁻¹' Set.Icc 0 1 = unit_box_1D.toSet :=
   preimage_Icc_eq_box 0 1
 
@@ -3462,7 +3463,7 @@ lemma Jordan_outer_unit_box : Jordan_outer_measure unit_box_1D.toSet = 1 := by
   rw [IsElementary.measure_of_box unit_box_1D]
   exact unit_box_volume
 
-/-- Closure of U contains the preimage of [0,1] -/
+/-- Closure of U contains the preimage of \[0,1\] -/
 lemma U_closure_contains_unit_box (ε : ℝ) (hε : 0 < ε) :
     unit_box_1D.toSet ⊆ closure (U ε) := by
   -- Key insight: For a homeomorphism f, closure(f⁻¹(S)) = f⁻¹(closure(S))
@@ -3490,7 +3491,7 @@ lemma U_closure_contains_unit_box (ε : ℝ) (hε : 0 < ε) :
     exact hy_U
 
 /-- Jordan outer measure of U ≥ 1.
-    Proof uses: density of ℚ → closure(U) ⊇ [0,1] → Jordan_outer(U) ≥ Jordan_outer([0,1]) = 1. -/
+    Proof uses: density of ℚ → closure(U) ⊇ \[0,1\] → Jordan\_outer(U) ≥ Jordan\_outer(\[0,1\]) = 1. -/
 lemma U_jordan_outer_ge (ε : ℝ) (hε : 0 < ε) :
     Jordan_outer_measure (U ε) ≥ 1 := by
   -- By JordanMeasurable.outer_measure_of_closure, Jordan_outer(closure U) = Jordan_outer(U)
@@ -3505,15 +3506,15 @@ lemma U_jordan_outer_ge (ε : ℝ) (hε : 0 < ε) :
     _ = Jordan_outer_measure (U ε) := h_closure_eq
 
 /-- Lebesgue outer measure of U ≤ 2ε (countable subadditivity).
-    U = ⋃_n (q_n - ε/2^{n+1}, q_n + ε/2^{n+1}), each interval has length 2ε/2^{n+1},
-    and ∑ 2ε/2^{n+1} = 2ε.
+    U = ⋃\_n (q\_n - ε/2^\{n+1\}, q\_n + ε/2^\{n+1\}), each interval has length 2ε/2^\{n+1\},
+    and ∑ 2ε/2^\{n+1\} = 2ε.
 
     Proof structure:
-    1. Express U as countable union: U = ⋃_n E_n
-    2. By countable subadditivity (union_le): m*(U) ≤ ∑' m*(E_n)
-    3. Each component bounded: m*(E_n) ≤ 2ε/2^{n+1} (component_lebesgue_le)
-    4. Geometric sum: ∑' 2ε/2^{n+1} = 2ε (tsum_interval_lengths)
-    5. EReal tsum comparison: ∑' m*(E_n) ≤ ∑' (2ε/2^{n+1}) = 2ε -/
+    1. Express U as countable union: U = ⋃\_n E\_n
+    2. By countable subadditivity (union\_le): m\*(U) ≤ ∑' m\*(E\_n)
+    3. Each component bounded: m\*(E\_n) ≤ 2ε/2^\{n+1\} (component\_lebesgue\_le)
+    4. Geometric sum: ∑' 2ε/2^\{n+1\} = 2ε (tsum\_interval\_lengths)
+    5. {name}`EReal` tsum comparison: ∑' m\*(E\_n) ≤ ∑' (2ε/2^\{n+1\}) = 2ε -/
 lemma U_lebesgue_le (ε : ℝ) (hε : 0 < ε) :
     Lebesgue_outer_measure (U ε) ≤ ((2 * ε : ℝ) : EReal) := by
   -- U = ⋃_n (component intervals in EuclideanSpace' 1)
@@ -3555,10 +3556,10 @@ end Remark_1_2_8
 -- ========================================================================
 
 /-- Remark 1.2.8: There exists a bounded open set that is not Jordan measurable.
-    Proof sketch: Take U = ⋃_{n} (q_n - ε/2^{n+1}, q_n + ε/2^{n+1}) where {q_n} enumerates ℚ ∩ [0,1].
-    U is open and bounded. By countable subadditivity, m*(U) ≤ 2ε.
-    By density of ℚ, closure(U) ⊇ [0,1], so m*,J(U) ≥ 1.
-    For ε = 1/3, we get m*(U) ≤ 2/3 < 1 ≤ m*,J(U), contradicting Jordan measurability. -/
+    Proof sketch: Take U = ⋃\_\{n\} (q\_n - ε/2^\{n+1\}, q\_n + ε/2^\{n+1\}) where \{q\_n\} enumerates ℚ ∩ \[0,1\].
+    U is open and bounded. By countable subadditivity, m\*(U) ≤ 2ε.
+    By density of ℚ, closure(U) ⊇ \[0,1\], so m\*,J(U) ≥ 1.
+    For ε = 1/3, we get m\*(U) ≤ 2/3 < 1 ≤ m\*,J(U), contradicting Jordan measurability. -/
 example : ∃ (E: Set (EuclideanSpace' 1)), Bornology.IsBounded E ∧
     IsOpen E ∧ ¬ JordanMeasurable E := by
   use Remark_1_2_8.U (1/3)
@@ -3612,7 +3613,7 @@ example : ∃ (E: Set (EuclideanSpace' 1)), Bornology.IsBounded E ∧
   -- Contradiction: 1 ≤ Jordan_inner ≤ 2/3 is impossible
   linarith
 
-/-- Remark 1.2.8: The complement of U in [-2,2] is compact but not Jordan measurable. -/
+/-- Remark 1.2.8: The complement of U in \[-2,2\] is compact but not Jordan measurable. -/
 example : ∃ (E: Set (EuclideanSpace' 1)), Bornology.IsBounded E ∧
     IsCompact E ∧ ¬ JordanMeasurable E := by
   -- Let B = [-2, 2] lifted to EuclideanSpace' 1
@@ -3861,7 +3862,7 @@ lemma IsElementary.measure_of_almostDisjUnion {d:ℕ} {E F: Set (EuclideanSpace'
   -- Final step: combine everything
   rw [← h_measure_eq, h_decomp_measure, h_sdiff_measure]
 
-/-- Split a Fin (n+1) indexed union into a Fin n indexed union plus the last element.
+/-- Split a {lean}`Fin (n+1)` indexed union into a {lean}`Fin n` indexed union plus the last element.
     This is a general helper for induction on finite unions. -/
 lemma Fin.iUnion_succ_eq_union_last {α : Type*} {n : ℕ} (f : Fin (n + 1) → Set α) :
     (⋃ i, f i) = (⋃ i : Fin n, f (Fin.castSucc i)) ∪ f (Fin.last n) := by
@@ -3900,9 +3901,9 @@ lemma AlmostDisjoint.castSucc_last {d n : ℕ} {B : Fin (n + 1) → Box d}
   rw [heq] at h1
   simp at h1
 
-/-- For any BoundedInterval, interior (closure I) ⊆ closure (interior I).
-    This holds because all interval types (Ioo, Icc, Ioc, Ico) have closure = Icc
-    and interior = Ioo, so interior(closure(I)) = Ioo ⊆ Icc = closure(interior(I)). -/
+/-- For any {name}`BoundedInterval`, interior (closure I) ⊆ closure (interior I).
+    This holds because all interval types ({name}`BoundedInterval.Ioo`, {name}`BoundedInterval.Icc`, {name}`BoundedInterval.Ioc`, {name}`BoundedInterval.Ico`) have closure = {name}`BoundedInterval.Icc`
+    and interior = {name}`BoundedInterval.Ioo`, so interior(closure(I)) = {name}`BoundedInterval.Ioo` ⊆ {name}`BoundedInterval.Icc` = closure(interior(I)). -/
 lemma BoundedInterval.interior_closure_subset_closure_interior (I : BoundedInterval) :
     interior (closure (I : Set ℝ)) ⊆ closure (interior (I : Set ℝ)) := by
   cases I with
@@ -3933,7 +3934,7 @@ lemma BoundedInterval.interior_closure_subset_closure_interior (I : BoundedInter
     · simp only [Set.Ico_eq_empty hab, closure_empty, interior_empty]; exact Set.empty_subset _
 
 /-- For any box, the interior of its frontier is empty. This holds regardless of whether
-    the box uses closed intervals (Icc), open intervals (Ioo), or half-open intervals,
+    the box uses closed intervals ({name}`BoundedInterval.Icc`), open intervals ({name}`BoundedInterval.Ioo`), or half-open intervals,
     because the frontier of a box is a lower-dimensional set (union of faces). -/
 lemma Box.interior_frontier_eq_empty {d : ℕ} (B : Box d) : interior (frontier B.toSet) = ∅ := by
   rw [Box.frontier_toSet, ← (PiLp.homeomorph 2 (fun _ : Fin d => ℝ)).preimage_interior]
@@ -3947,7 +3948,7 @@ lemma Box.interior_frontier_eq_empty {d : ℕ} (B : Box d) : interior (frontier
   exact Set.pi_mono (fun i _ => BoundedInterval.interior_closure_subset_closure_interior _) hx1
 
 /-- The interior of a finite union of box frontiers is empty. This is because each box frontier
-    is a closed set with empty interior, and we can apply `interior_union_isClosed_of_interior_empty`
+    is a closed set with empty interior, and we can apply {name}`interior_union_isClosed_of_interior_empty`
     iteratively. -/
 lemma interior_iUnion_Box_frontier_eq_empty {d n : ℕ} (B : Fin n → Box d) :
     interior (⋃ i, frontier (B i).toSet) = ∅ := by
@@ -4069,7 +4070,7 @@ theorem IsElementary.almost_disjoint {d k:ℕ} {E: Set (EuclideanSpace' d)} (hE:
     -- Final computation
     rw [Fin.sum_univ_castSucc, h_measure_eq, h_measure_add, hE'_measure, h_B_last_measure]
 
-/-- Restricting pairwise almost-disjoint from ℕ to Fin N preserves the property. -/
+/-- Restricting pairwise almost-disjoint from ℕ to {lean}`Fin N` preserves the property. -/
 lemma AlmostDisjoint.restrict_fin {d : ℕ} {B : ℕ → Box d}
     (h : Pairwise (Function.onFun AlmostDisjoint B)) (N : ℕ) :
     Pairwise (Function.onFun AlmostDisjoint (fun i : Fin N => B i.val)) := by
@@ -4079,8 +4080,8 @@ lemma AlmostDisjoint.restrict_fin {d : ℕ} {B : ℕ → Box d}
   intro heq
   exact hij (Fin.ext heq)
 
-/-- For nonneg Real sequences, if all partial sums are ≤ c (an EReal bound), then tsum ≤ c.
-    This is the converse direction of `EReal.finset_sum_le_tsum`. -/
+/-- For nonneg Real sequences, if all partial sums are ≤ c (an {name}`EReal` bound), then {name}`tsum` ≤ c.
+    This is the converse direction of {name}`EReal.finset_sum_le_tsum`. -/
 lemma EReal.tsum_le_of_sum_range_le {f : ℕ → ℝ} {c : EReal}
     (hf : ∀ n, 0 ≤ f n) (h : ∀ N, (∑ i ∈ Finset.range N, f i : EReal) ≤ c) :
     ∑' n, (f n).toEReal ≤ c := by
@@ -4371,7 +4372,7 @@ def Box.IsDyadicAtScale {d:ℕ} (B: Box d) (n:ℤ) : Prop := ∃ a: Fin d → 
 
 def Box.IsDyadic {d:ℕ} (B: Box d) : Prop := ∃ n:ℕ, B.IsDyadicAtScale n
 
-/-- Dyadic boxes have all sides as closed intervals (Icc). -/
+/-- Dyadic boxes have all sides as closed intervals ({name}`BoundedInterval.Icc`). -/
 lemma Box.IsDyadic.all_sides_Icc {d : ℕ} {B : Box d} (hB : B.IsDyadic) :
     ∀ i, ∃ a b, B.side i = BoundedInterval.Icc a b := by
   obtain ⟨n, ⟨a, rfl⟩⟩ := hB
@@ -4862,10 +4863,10 @@ lemma dyadicCubeLargerNotInSmaller {d:ℕ} (hd : 0 < d) {n m : ℤ} (hnm : n < m
 /-- Lemma 1.2.11: Every open set is a countable union of almost disjoint dyadic cubes.
 Note: every dyadic cube is nonempty
     Proof outline:
-    1. For each x ∈ E, by exists_dyadic_cube_subset, there exists a dyadic cube containing x ⊆ E
-    2. The set of all such dyadic cubes is countable (subset of ℕ × (Fin d → ℤ))
+    1. For each x ∈ E, by {name}`IsOpen.exists_dyadic_cube_subset`, there exists a dyadic cube containing x ⊆ E
+    2. The set of all such dyadic cubes is countable (subset of {lean}`ℕ × (Fin d → ℤ)`)
     3. Take maximal cubes (not strictly contained in another cube in the collection)
-    4. By DyadicCube.nesting, distinct maximal cubes are almost disjoint
+    4. By {name}`DyadicCube.nesting`, distinct maximal cubes are almost disjoint
     5. E equals the union of these maximal cubes -/
 theorem IsOpen.eq_union_boxes {d:ℕ} (hd : 0 < d) (E: Set (EuclideanSpace' d)) (hE: IsOpen E)
     (hE_nonempty : E.Nonempty) :
@@ -5260,7 +5261,7 @@ theorem Lebesgue_outer_measure.of_open {d:ℕ} (E: Set (EuclideanSpace' d)) (hE:
       -- Apply lemma eq_Jordan_inner_of_boxes (Exercise 1.2.5)
       exact Lebesgue_outer_measure.eq_Jordan_inner_of_boxes E B hE_eq hB_disj
 
-/-- Lemma 1.2.12 (Outer regularity). m*(E) = inf{m*(U) : E ⊆ U, U open}. -/
+/-- Lemma 1.2.12 (Outer regularity). m\*(E) = inf\{m\*(U) : E ⊆ U, U open\}. -/
 theorem Lebesgue_outer_measure.eq {d:ℕ} (E: Set (EuclideanSpace' d)) : Lebesgue_outer_measure E = sInf { M | ∃ U, E ⊆ U ∧ IsOpen U ∧ M = Lebesgue_outer_measure U} := by
   let S := { M | ∃ U, E ⊆ U ∧ IsOpen U ∧ M = Lebesgue_outer_measure U}
   apply le_antisymm
diff --git a/analysis/Analysis/MeasureTheory/Section_1_2_2.lean b/Analysis/MeasureTheory/Section_1_2_2.lean
similarity index 98%
rename from analysis/Analysis/MeasureTheory/Section_1_2_2.lean
rename to Analysis/MeasureTheory/Section_1_2_2.lean
index 1d4a9b90..41c26639 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_2_2.lean
+++ b/Analysis/MeasureTheory/Section_1_2_2.lean
@@ -76,7 +76,7 @@ private lemma Lebesgue_outer_measure.sum_of_almost_disjoint_finset {d : ℕ} (_h
 
 /-- Helper: Bounded closed sets are measurable (Lemma 1.2.13(ii) for bounded case).
     For bounded closed E (compact by Heine-Borel), show that for any ε > 0,
-    there exists open U ⊇ E with m*(U \ E) ≤ ε. -/
+    there exists open U ⊇ E with m\*(U \ E) ≤ ε. -/
 private lemma IsClosed.measurable_of_bounded {d:ℕ} {E: Set (EuclideanSpace' d)}
     (hE: IsClosed E) (hE_bounded : Bornology.IsBounded E) : LebesgueMeasurable E := by
   intro ε hε
@@ -819,7 +819,7 @@ theorem LebesgueMeasurable.inter {d :ℕ} {E F: Set (EuclideanSpace' d)} (hE: Le
   rw [h_eq]
   exact LebesgueMeasurable.finite_inter hS
 
-/-- Finite intersection indexed by a Finset is Lebesgue measurable. -/
+/-- Finite intersection indexed by a {name}`Finset` is Lebesgue measurable. -/
 lemma LebesgueMeasurable.finset_inter {d : ℕ} {α : Type*} [DecidableEq α]
     {E : α → Set (EuclideanSpace' d)} {S : Finset α}
     (hE : ∀ i ∈ S, LebesgueMeasurable (E i)) :
@@ -844,7 +844,7 @@ lemma LebesgueMeasurable.finset_inter {d : ℕ} {α : Type*} [DecidableEq α]
         · exact h i hi']
     exact LebesgueMeasurable.inter hE_a (ih hE_rest)
 
-/-- Finite union indexed by a Finset is Lebesgue measurable. -/
+/-- Finite union indexed by a {name}`Finset` is Lebesgue measurable. -/
 lemma LebesgueMeasurable.finset_union {d : ℕ} {α : Type*} [DecidableEq α]
     {E : α → Set (EuclideanSpace' d)} {S : Finset α}
     (hE : ∀ i ∈ S, LebesgueMeasurable (E i)) :
@@ -928,7 +928,7 @@ theorem CantorSet.uncountable : Uncountable CantorSet := by
 
 theorem CantorSet.null : IsNull (Real.equiv_EuclideanSpace' '' CantorSet) := by sorry
 
-/-- Exercise 1.2.10 ([0,1) is not the countable union of pairwise disjoint closed intervals)-/
+/-- Exercise 1.2.10 (\[0,1) is not the countable union of pairwise disjoint closed intervals)-/
 example : ¬ ∃ (I: ℕ → BoundedInterval), (∀ n, IsClosed (I n).toSet) ∧ (Set.univ.PairwiseDisjoint (fun n ↦ (I n).toSet) ) ∧ (⋃ n, (I n).toSet = Set.Ico 0 1) := by
   sorry
 
@@ -946,7 +946,7 @@ theorem Lebesgue_measure.empty {d:ℕ} : Lebesgue_measure (∅: Set (EuclideanSp
   Lebesgue_outer_measure.of_empty d
 
 /-- Helper: Countable additivity for compact sets.
-    When all E_n are compact and pairwise disjoint, m(⋃ E_n) = ∑' m(E_n).
+    When all $`E_n` are compact and pairwise disjoint, $`m(⋃ E_n) = ∑' m(E_n)`.
     Key: compact disjoint sets have positive separation, so we can use Lemma 1.2.5. -/
 private lemma Lebesgue_measure.countable_union_compact {d:ℕ} (hd : 0 < d)
     {E: ℕ → Set (EuclideanSpace' d)}
@@ -1054,9 +1054,9 @@ private lemma Lebesgue_measure.countable_union_compact {d:ℕ} (hd : 0 < d)
 
 /-- Helper: Countable additivity for bounded sets.
     Following the textbook approach: Use ε/2ⁿ trick with inner regularity (Exercise 1.2.7).
-    For bounded measurable E_n, find compact K_n ⊆ E_n with m(E_n) ≤ m(K_n) + ε/2^{n+1}.
-    The K_n are pairwise disjoint (since K_n ⊆ E_n), so m(⋃ K_n) = ∑' m(K_n) by compact case,
-    and m(⋃ E_n) ≥ m(⋃ K_n) = ∑' m(K_n) ≥ ∑' m(E_n) - ε. Let ε → 0. -/
+    For bounded measurable $`E_n`, find compact $`K_n ⊆ E_n` with $`m(E_n) ≤ m(K_n) + ε/2^(n+1)`.
+    The $`K_n` are pairwise disjoint (since $`K_n ⊆ E_n`), so $`m(⋃ K_n) = ∑' m(K_n)` by compact case,
+    and $`m(⋃ E_n) ≥ m(⋃ K_n) = ∑' m(K_n) ≥ ∑' m(E_n) - ε`. Let ε → 0. -/
 private lemma Lebesgue_measure.countable_union_bounded {d:ℕ} (hd : 0 < d)
     {E: ℕ → Set (EuclideanSpace' d)}
     (hmes: ∀ n, LebesgueMeasurable (E n))
@@ -1249,10 +1249,10 @@ private lemma Lebesgue_measure.countable_union_bounded {d:ℕ} (hd : 0 < d)
   exact le_antisymm h_le h_ge
 
 /-- Lemma 1.2.15(b) (Countable additivity).
-    Strategy: m(⋃ E_n) = ∑' m(E_n) for pairwise disjoint measurable sets.
-    - Direction ≤: Countable subadditivity (Lebesgue_outer_measure.union_le)
-    - Direction ≥: Decompose ℝᵈ into annuli Aₘ, express each E_n = ⋃_m (E_n ∩ Aₘ),
-      apply bounded case to the doubly-indexed family (E_n ∩ Aₘ). -/
+    Strategy: `m(⋃ E_n) = ∑' m(E_n)` for pairwise disjoint measurable sets.
+    - Direction ≤: Countable subadditivity ({name}`Lebesgue_outer_measure.union_le`)
+    - Direction ≥: Decompose ℝᵈ into annuli Aₘ, express each `E_n = ⋃_m (E_n ∩ Aₘ)`,
+      apply bounded case to the doubly-indexed family $`(E_n ∩ Aₘ)`. -/
 theorem Lebesgue_measure.countable_union {d:ℕ} {E: ℕ → Set (EuclideanSpace' d)} (hmes: ∀ n, LebesgueMeasurable (E n)) (hdisj: Set.univ.PairwiseDisjoint E) : Lebesgue_measure (⋃ n, E n) = ∑' n, Lebesgue_measure (E n) := by
   -- Direction ≤: Countable subadditivity
   have h_le : Lebesgue_measure (⋃ n, E n) ≤ ∑' n, Lebesgue_measure (E n) :=
diff --git a/analysis/Analysis/MeasureTheory/Section_1_2_3.lean b/Analysis/MeasureTheory/Section_1_2_3.lean
similarity index 96%
rename from analysis/Analysis/MeasureTheory/Section_1_2_3.lean
rename to Analysis/MeasureTheory/Section_1_2_3.lean
index f45c3e75..bb736ad8 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_2_3.lean
+++ b/Analysis/MeasureTheory/Section_1_2_3.lean
@@ -12,7 +12,7 @@ open scoped Pointwise
 /-! ## Vitali Set Construction
 
 We construct a Vitali set by choosing representatives from each coset of ℝ/ℚ
-that intersects [0,1]. The key is that ℚ acts on ℝ by translation, and this
+that intersects \[0,1\]. The key is that ℚ acts on ℝ by translation, and this
 partitions ℝ into countably many disjoint translates of any transversal.
 -/
 
@@ -30,7 +30,7 @@ def Rat.addSubgroup : AddSubgroup ℝ where
 /-- The quotient group ℝ/ℚ (reals modulo rationals) -/
 abbrev RealModRat := ℝ ⧸ Rat.addSubgroup
 
-/-- ℚ is dense in ℝ, so every coset of ℝ/ℚ intersects [0,1] -/
+/-- ℚ is dense in ℝ, so every coset of ℝ/ℚ intersects \[0,1\] -/
 lemma coset_intersects_unit_interval (c : RealModRat) :
     ∃ x : ℝ, x ∈ Set.Icc 0 1 ∧ QuotientAddGroup.mk (s := Rat.addSubgroup) x = c := by
   obtain ⟨r⟩ := c
@@ -62,17 +62,17 @@ lemma coset_intersects_unit_interval (c : RealModRat) :
     rw [heq]
     rfl
 
-/-- The Vitali set: choose one representative from each coset that lies in [0,1] -/
+/-- The Vitali set: choose one representative from each coset that lies in \[0,1\] -/
 noncomputable def VitaliSet : Set ℝ :=
   Set.range (fun c : RealModRat => (coset_intersects_unit_interval c).choose)
 
-/-- Each element of the Vitali set is in [0,1] -/
+/-- Each element of the Vitali set is in \[0,1\] -/
 lemma VitaliSet_subset_unit_interval : VitaliSet ⊆ Set.Icc 0 1 := by
   intro x hx
   obtain ⟨c, rfl⟩ := hx
   exact (coset_intersects_unit_interval c).choose_spec.1
 
-/-- Key lemma: [0,1] is covered by translates of E by rationals in [-1,1] -/
+/-- Key lemma: \[0,1\] is covered by translates of E by rationals in \[-1,1\] -/
 lemma unit_interval_covered_by_translates :
     Set.Icc (0:ℝ) 1 ⊆ ⋃ (q : ℚ) (_ : q ∈ Set.Icc (-1:ℚ) 1), (VitaliSet + {(q:ℝ)}) := by
   intro y hy
@@ -117,11 +117,11 @@ lemma unit_interval_covered_by_translates :
   · rfl
   · linarith [hy_eq]
 
-/-- The rationals in [-1,1] are countable -/
+/-- The rationals in \[-1,1\] are countable -/
 lemma rat_Icc_countable : Set.Countable {q : ℚ | q ∈ Set.Icc (-1:ℚ) 1} := by
   exact Set.countable_univ.mono (Set.subset_univ _)
 
-/-- The Lebesgue measure of a closed interval [a,b] in ℝ (embedded in EuclideanSpace' 1) equals b - a -/
+/-- The Lebesgue measure of a closed interval \[a,b\] in ℝ (embedded in {lean}`EuclideanSpace' 1`) equals b - a -/
 lemma Lebesgue_measure.Icc_eq (a b : ℝ) (hab : a ≤ b) :
     Lebesgue_measure (Real.equiv_EuclideanSpace' '' Set.Icc a b) = (b - a : ℝ) := by
   -- Use the fact that Set.Icc a b = (BoundedInterval.Icc a b).toSet
@@ -140,7 +140,7 @@ lemma Lebesgue_measure.Icc_eq (a b : ℝ) (hab : a ≤ b) :
   -- max (b - a) 0 = b - a since a ≤ b
   rw [max_eq_left (sub_nonneg.mpr hab)]
 
-/-- The Vitali set (lifted to EuclideanSpace' 1) is not Lebesgue measurable.
+/-- The Vitali set (lifted to {lean}`EuclideanSpace' 1`) is not Lebesgue measurable.
     This is the core of Proposition 1.2.18. -/
 theorem VitaliSet.nonmeasurable : ¬ LebesgueMeasurable (Real.equiv_EuclideanSpace' '' VitaliSet) := by
   let E := Real.equiv_EuclideanSpace' '' VitaliSet
diff --git a/analysis/Analysis/MeasureTheory/Section_1_3_1.lean b/Analysis/MeasureTheory/Section_1_3_1.lean
similarity index 98%
rename from analysis/Analysis/MeasureTheory/Section_1_3_1.lean
rename to Analysis/MeasureTheory/Section_1_3_1.lean
index 43a3f50a..38cc4ca6 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_3_1.lean
+++ b/Analysis/MeasureTheory/Section_1_3_1.lean
@@ -171,7 +171,7 @@ lemma ComplexSimpleFunction.conj {d:ℕ} {f: EuclideanSpace' d → ℂ} (hf: Com
 
 noncomputable def UnsignedSimpleFunction.integ {d:ℕ} {f: EuclideanSpace' d → EReal} (hf: UnsignedSimpleFunction f) : EReal := ∑ i, (hf.choose_spec.choose i) * Lebesgue_measure (hf.choose_spec.choose_spec.choose i)
 
-/-! ### Helper lemmas for Lemma 1.3.4
+/-! ## Helper lemmas for Lemma 1.3.4
 
 The proof uses a Venn diagram argument: given two representations of the same simple function,
 we partition R^d into atoms (intersections of all sets and their complements), express each
@@ -182,14 +182,14 @@ namespace UnsignedSimpleFunction.IntegralWellDef
 
 open scoped Classical
 
-/-- Given families of sets indexed by Fin k and Fin k', an atom is determined by
-    a choice of "in" or "out" for each set. We encode this as a Fin (2^(k+k')) index. -/
+/-- {given -show}`k, k'` Given families of sets indexed by {lean}`Fin k` and {lean}`Fin k'`, an atom is determined by
+    a choice of “in” or “out” for each set. We encode this as a {lean}`Fin (2^(k+k'))` index. -/
 def atomMembership (_k _k' : ℕ) (n : ℕ) (i : ℕ) : Bool := (n / 2^i) % 2 = 1
 
 lemma atomMembership_eq_testBit (k k' n i : ℕ) : atomMembership k k' n i = n.testBit i := by
   simp only [atomMembership, Nat.testBit_eq_decide_div_mod_eq]
 
-/-- The atom indexed by n is the intersection over all i of (E_i if bit i is 1, else E_i^c) -/
+/-- The atom indexed by n is the intersection over all $`i` of ($`E_i` if bit $`i` is 1, else $`E_i^c`) -/
 def atom {X : Type*} {k k' : ℕ} (E : Fin k → Set X) (E' : Fin k' → Set X) (n : Fin (2^(k+k'))) : Set X :=
   {x | (∀ i : Fin k, atomMembership k k' n i ↔ x ∈ E i) ∧
        (∀ i : Fin k', atomMembership k k' n (k + i) ↔ x ∈ E' i)}
@@ -255,7 +255,7 @@ private lemma sum_pow_two_range (n : ℕ) : ∑ i ∈ Finset.range n, (2:ℕ)^i
     have h : 1 ≤ 2^n := Nat.one_le_two_pow
     omega
 
-/-- For any subset of Fin k, sum of 2^j.val is less than 2^k -/
+/-- For any subset of {lean}`Fin k`, sum of {given -show (type := "Fin k")}`j` {lean}`2^j.val` is less than {lean}`2^k` -/
 private lemma sum_pow_two_fin_lt {k : ℕ} {s : Finset (Fin k)} :
     s.sum (fun j => (2:ℕ)^j.val) < 2^k := by
   have h1 : s.sum (fun j => (2:ℕ)^j.val) ≤ Finset.univ.sum (fun j : Fin k => (2:ℕ)^j.val) := by
@@ -345,7 +345,7 @@ lemma atomIndexOf_testBit_E' {X : Type*} [DecidableEq X] {k k' : ℕ} (E : Fin k
   rw [hsub, Nat.testBit_sum_pow_two_fin]
   simp only [Finset.mem_filter, Finset.mem_univ, true_and]
 
-/-- Original set E_i is the union of atoms where bit i is 1 -/
+/-- Original set E\_i is the union of atoms where bit i is 1 -/
 lemma set_eq_biUnion_atoms {X : Type*} {k k' : ℕ} (E : Fin k → Set X) (E' : Fin k' → Set X) (i : Fin k) :
     E i = ⋃ n ∈ {n : Fin (2^(k+k')) | atomMembership k k' n i}, atom E E' n := by
   classical
@@ -370,7 +370,7 @@ lemma set_eq_biUnion_atoms {X : Type*} {k k' : ℕ} (E : Fin k → Set X) (E' :
     obtain ⟨n, hn_bit, hx_atom⟩ := hx
     exact (hx_atom.1 i).mp hn_bit
 
-/-- Original set E'_i is the union of atoms where bit (k+i) is 1 -/
+/-- Original set E'\_i is the union of atoms where bit (k+i) is 1 -/
 lemma set_eq_biUnion_atoms' {X : Type*} {k k' : ℕ} (E : Fin k → Set X) (E' : Fin k' → Set X) (i : Fin k') :
     E' i = ⋃ n ∈ {n : Fin (2^(k+k')) | atomMembership k k' n (k + i)}, atom E E' n := by
   classical
@@ -718,7 +718,7 @@ lemma weightedMeasureSum_eq_of_eq {d k k' : ℕ}
         congr 1; ext i; congr 1; exact (hmes_decomp' i).symm
     _ = weightedMeasureSum c' E' := rfl
 
-/-! ### Single-family atoms (k' = 0 specialization)
+/-! ## Single-family atoms (k' = 0 specialization)
 
 When working with a single family of sets (no second family to compare against),
 we specialize the atom machinery with k' = 0. -/
@@ -1083,7 +1083,7 @@ def RealSimpleFunction.AbsolutelyIntegrable {d:ℕ} {f: EuclideanSpace' d → 
 def ComplexSimpleFunction.AbsolutelyIntegrable {d:ℕ} {f: EuclideanSpace' d → ℂ} (hf: ComplexSimpleFunction f) : Prop :=
   (hf.abs).integ < ⊤
 
-/-! ### Disjoint representation for RealSimpleFunction
+/-! ## Disjoint representation for {name}`RealSimpleFunction`
 
 Measure-theory specific lemmas for the disjoint representation of simple functions. -/
 
@@ -1134,7 +1134,7 @@ lemma eq_sum_atomValue_indicator {d k : ℕ} (c : Fin k → ℝ) (E : Fin k →
 
 end RealSimpleFunction.DisjointRepr
 
-/-- Disjoint representation: any RealSimpleFunction has an equivalent representation
+/-- Disjoint representation: any {name}`RealSimpleFunction` has an equivalent representation
     with pairwise disjoint, measurable sets. -/
 lemma RealSimpleFunction.disjoint_representation {d:ℕ} {f: EuclideanSpace' d → ℝ} (hf: RealSimpleFunction f) :
     ∃ (n:ℕ) (v: Fin n → ℝ) (A: Fin n → Set (EuclideanSpace' d)),
@@ -1272,20 +1272,20 @@ lemma ComplexSimpleFunction.AbsolutelyIntegrable.smul {d:ℕ} {f: EuclideanSpace
 lemma ComplexSimpleFunction.AbsolutelyIntegrable.conj {d:ℕ} {f: EuclideanSpace' d → ℂ} {hf: ComplexSimpleFunction f} (hf_integ: hf.AbsolutelyIntegrable) :
   (hf.conj).AbsolutelyIntegrable := by sorry
 
-/-- Exercise 1.3.2 (i) (*-linearity) -/
+/-- Exercise 1.3.2 (i) ({lit}`*`-linearity) -/
 lemma RealSimpleFunction.integ_add {d:ℕ} {f g: EuclideanSpace' d → ℝ} {hf: RealSimpleFunction f} {hg: RealSimpleFunction g} (hf_integ: hf.AbsolutelyIntegrable) (hg_integ: hg.AbsolutelyIntegrable) : (hf.add hg).integ = hf.integ + hg.integ := by sorry
 
 lemma ComplexSimpleFunction.integ_add {d:ℕ} {f g: EuclideanSpace' d → ℂ} {hf: ComplexSimpleFunction f} {hg: ComplexSimpleFunction g} (hf_integ: hf.AbsolutelyIntegrable) (hg_integ: hg.AbsolutelyIntegrable) : (hf.add hg).integ = hf.integ + hg.integ := by
   sorry
 
-/-- Exercise 1.3.2 (i) (*-linearity) -/
+/-- Exercise 1.3.2 (i) ({lit}`*`-linearity) -/
 lemma RealSimpleFunction.integ_smul {d:ℕ} {f: EuclideanSpace' d → ℝ} {hf: RealSimpleFunction f} (hf_integ: hf.AbsolutelyIntegrable) (a: ℝ) : (hf.smul a).integ = a * hf.integ := by
   sorry
 
 lemma ComplexSimpleFunction.integ_smul {d:ℕ} {f: EuclideanSpace' d → ℂ} {hf: ComplexSimpleFunction f} (hf_integ: hf.AbsolutelyIntegrable) (a: ℂ) : (hf.smul a).integ = a * hf.integ := by
   sorry
 
-/-- Exercise 1.3.2 (i) (*-linearity) -/
+/-- Exercise 1.3.2 (i) ({lit}`*`-linearity) -/
 lemma ComplexSimpleFunction.integral_conj {d:ℕ} {f: EuclideanSpace' d → ℂ} {hf: ComplexSimpleFunction f} (hf_integ: hf.AbsolutelyIntegrable) : (hf.conj).integ = (starRingEnd ℂ) hf.integ := by
   sorry
 
diff --git a/analysis/Analysis/MeasureTheory/Section_1_3_2.lean b/Analysis/MeasureTheory/Section_1_3_2.lean
similarity index 97%
rename from analysis/Analysis/MeasureTheory/Section_1_3_2.lean
rename to Analysis/MeasureTheory/Section_1_3_2.lean
index 239fa7cf..3ed3b1a2 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_3_2.lean
+++ b/Analysis/MeasureTheory/Section_1_3_2.lean
@@ -1,6 +1,8 @@
 import Analysis.MeasureTheory.Section_1_3_1
 import Mathlib.Algebra.Order.Floor.Semifield
 
+set_option doc.verso.suggestions false
+
 /-!
 # Introduction to Measure Theory, Section 1.3.2: Measurable functions
 
@@ -12,7 +14,7 @@ def Unsigned {X Y:Type*} [LE Y] [Zero Y] (f:X → Y) : Prop := ∀ x, f x ≥ 0
 
 def PointwiseConvergesTo {X Y:Type*} [TopologicalSpace Y] (f: ℕ → X → Y) (g: X → Y) : Prop := ∀ x, Filter.atTop.Tendsto (fun n ↦ f n x) (nhds (g x))
 
-/-- Definiiton 1.3.8 (Unsigned measurable function) -/
+/-- Definition 1.3.8 (Unsigned measurable function) -/
 def UnsignedMeasurable {d:ℕ} (f: EuclideanSpace' d → EReal) : Prop := Unsigned f ∧ ∃ (g: ℕ → EuclideanSpace' d → EReal), (∀ n, UnsignedSimpleFunction (g n)) ∧ (PointwiseConvergesTo g f)
 
 def EReal.BoundedFunction {X:Type*} (f:X → EReal) : Prop := ∃ M:NNReal, ∀ x, (f x).abs ≤ M
@@ -28,9 +30,9 @@ The proof follows the book's implication chain. We establish explicit edges and
 let `tfae_finish` compute the transitive closure.
 
 **Explicit edges declared:**
-- (i) ⟺ (ii): by definition of UnsignedMeasurable
+- (i) ⟺ (ii): by definition of {name}`UnsignedMeasurable`
 - (ii) ⟹ (iii): pointwise everywhere implies pointwise a.e.
-- (iv) ⟹ (ii): monotone sequences in [0,∞] converge to their supremum
+- (iv) ⟹ (ii): monotone sequences in \[0,∞\] converge to their supremum
 - (iii) ⟹ (v): via limsup representation (main technical work)
 - (v) ⟺ (vi): countable unions/intersections
 - (vi) ⟺ (vii): complementation
@@ -38,10 +40,10 @@ let `tfae_finish` compute the transitive closure.
 - (v)-(viii) ⟹ (ix): intervals are intersections of half-intervals
 - (ix) ⟹ (x): open sets are countable unions of intervals
 - (x) ⟺ (xi): complementation
-- (x) ⟹ (vii): {f < λ} = f⁻¹'(Iio λ) and Iio λ is open
+- (x) ⟹ (vii): \{f < λ\} = f⁻¹'({name}`Set.Iio` λ) and {name}`Set.Iio` λ is open
 - (v)-(xi) ⟹ (iv): construction of approximating sequence
 
-**Derived transitively (by tfae_finish):**
+**Derived transitively (by `tfae_finish`):**
 - (ix) ⟹ (v) or (vi): via (ix) → (x) → (vii) → (vi) → (v)
 - (x) ⟹ (v)-(ix): via (x) → (vii) → (vi) → (v) → (viii)/(ix)
 -/
@@ -66,7 +68,7 @@ private abbrev stmt_ix (f : EuclideanSpace' d → EReal) := ∀ I:BoundedInterva
 private abbrev stmt_x (f : EuclideanSpace' d → EReal) := ∀ U: Set EReal, IsOpen U → LebesgueMeasurable (f⁻¹' U)
 private abbrev stmt_xi (f : EuclideanSpace' d → EReal) := ∀ K: Set EReal, IsClosed K → LebesgueMeasurable (f⁻¹' K)
 
-/-! ### (i) ⟺ (ii): By definition of UnsignedMeasurable -/
+/-! # (i) ⟺ (ii): By definition of {name}`UnsignedMeasurable` -/
 
 private lemma i_iff_ii (hf : Unsigned f) : stmt_i f ↔ stmt_ii f := by
   simp only [UnsignedMeasurable]
@@ -76,7 +78,7 @@ private lemma i_iff_ii (hf : Unsigned f) : stmt_i f ↔ stmt_ii f := by
   · intro ⟨g, hg_simple, hg_conv⟩
     exact ⟨hf, g, hg_simple, hg_conv⟩
 
-/-! ### (ii) ⟹ (iii): Pointwise everywhere implies pointwise a.e. -/
+/-! # (ii) ⟹ (iii): Pointwise everywhere implies pointwise a.e. -/
 
 private lemma ii_imp_iii : stmt_ii f → stmt_iii f := by
   intro ⟨g, hg_simple, hg_conv⟩
@@ -91,7 +93,7 @@ private lemma ii_imp_iii : stmt_ii f → stmt_iii f := by
   rw [h_empty]
   exact Lebesgue_outer_measure.of_empty d
 
-/-! ### (iv) ⟹ (ii): Monotone sequences in [0,∞] converge to their supremum -/
+/-! # (iv) ⟹ (ii): Monotone sequences in \[0,∞\] converge to their supremum -/
 
 private lemma iv_imp_ii : stmt_iv f → stmt_ii f := by
   intro ⟨g, hg_props, hg_mono, hg_sup⟩
@@ -101,7 +103,7 @@ private lemma iv_imp_ii : stmt_iv f → stmt_ii f := by
   -- For monotone sequences in EReal, g n x → iSup (g · x)
   exact tendsto_atTop_iSup (hg_mono x)
 
-/-! ### (iii) ⟹ (v): Via limsup representation -/
+/-! # (iii) ⟹ (v): Via limsup representation -/
 
 -- Helper: Set.indicator' equals 1 when x ∈ E
 private lemma Set.indicator'_eq_one' {X : Type*} {E : Set X} {x : X} (hx : x ∈ E) :
@@ -420,7 +422,7 @@ private lemma iii_imp_v : stmt_iii f → stmt_v f := by
       exact (lt_irrefl _) (lt_trans (hN₀ n hn_ge) hn_gt)
   exact LebesgueMeasurable.of_ae_eq hE_meas hN_null h_ae_eq
 
-/-! ### (v) ⟹ (vi): {f ≥ λ} = ⋂_{n≥1} {f > λ - 1/n} -/
+/-! # (v) ⟹ (vi): \{f ≥ λ\} = ⋂\_\{n≥1\} \{f > λ - 1/n\} -/
 
 -- Helper: if x > n for all n ∈ ℕ, then x = ⊤
 private lemma EReal.eq_top_of_forall_nat_lt {x : EReal} (h : ∀ n : ℕ, x > n) : x = ⊤ := by
@@ -515,7 +517,7 @@ private lemma v_imp_vi : stmt_v f → stmt_vi f := by
       rw [h_eq]
       exact LebesgueMeasurable.countable_inter (fun n => hv _)
 
-/-! ### (vi) ⟹ (v): {f > λ} = ⋃_{q ∈ ℚ, q > λ} {f ≥ q} -/
+/-! # (vi) ⟹ (v): \{f > λ\} = ⋃\_\{q ∈ ℚ, q > λ\} \{f ≥ q\} -/
 
 private lemma vi_imp_v : stmt_vi f → stmt_v f := by
   intro hvi t
@@ -564,7 +566,7 @@ private lemma vi_imp_v : stmt_vi f → stmt_v f := by
     · exact hvi ((q : ℝ) : EReal)
     · exact LebesgueMeasurable.empty
 
-/-! ### (v) ⟹ (viii): {f ≤ t} = {f > t}ᶜ -/
+/-! # (v) ⟹ (viii): \{f ≤ t\} = \{f > t\}ᶜ -/
 
 private lemma v_imp_viii : stmt_v f → stmt_viii f := by
   intro hv t
@@ -572,7 +574,7 @@ private lemma v_imp_viii : stmt_v f → stmt_viii f := by
   rw [h_eq]
   exact (hv t).complement
 
-/-! ### (vi) ⟹ (vii): {f < t} = {f ≥ t}ᶜ -/
+/-! # (vi) ⟹ (vii): \{f < t\} = \{f ≥ t\}ᶜ -/
 
 private lemma vi_imp_vii : stmt_vi f → stmt_vii f := by
   intro hvi t
@@ -580,7 +582,7 @@ private lemma vi_imp_vii : stmt_vi f → stmt_vii f := by
   rw [h_eq]
   exact (hvi t).complement
 
-/-! ### (vii) ⟹ (vi): {f ≥ t} = {f < t}ᶜ -/
+/-! # (vii) ⟹ (vi): \{f ≥ t\} = \{f < t\}ᶜ -/
 
 private lemma vii_imp_vi : stmt_vii f → stmt_vi f := by
   intro hvii t
@@ -588,7 +590,7 @@ private lemma vii_imp_vi : stmt_vii f → stmt_vi f := by
   rw [h_eq]
   exact (hvii t).complement
 
-/-! ### (viii) ⟹ (v): {f > t} = {f ≤ t}ᶜ -/
+/-! # (viii) ⟹ (v): \{f > t\} = \{f ≤ t\}ᶜ -/
 
 private lemma viii_imp_v : stmt_viii f → stmt_v f := by
   intro hviii t
@@ -596,7 +598,7 @@ private lemma viii_imp_v : stmt_viii f → stmt_v f := by
   rw [h_eq]
   exact (hviii t).complement
 
-/-! ### (v)-(viii) ⟹ (ix): Intervals are intersections of half-intervals -/
+/-! # (v)-(viii) ⟹ (ix): Intervals are intersections of half-intervals -/
 
 private lemma v_to_viii_imp_ix (hv : stmt_v f) (hvi : stmt_vi f) (hvii : stmt_vii f) (hviii : stmt_viii f) :
     stmt_ix f := by
@@ -635,7 +637,7 @@ private lemma v_to_viii_imp_ix (hv : stmt_v f) (hvi : stmt_vi f) (hvii : stmt_vi
     rw [h_eq]
     exact (hvi _).inter (hvii _)
 
-/-! ### (ix) ⟹ (x): Open sets are countable unions of intervals -/
+/-! # (ix) ⟹ (x): Open sets are countable unions of intervals -/
 
 -- For unsigned f, f⁻¹'({⊥}) = ∅
 private lemma unsigned_preimage_bot_empty (hf : Unsigned f) : f⁻¹' {⊥} = ∅ := by
@@ -828,7 +830,7 @@ private lemma ix_imp_x (hf : Unsigned f) : stmt_ix f → stmt_x f := by
   · rw [Set.preimage_inter, unsigned_preimage_bot_empty hf, Set.inter_empty]
     exact LebesgueMeasurable.empty
 
-/-! ### (x) ⟺ (xi): Complementation -/
+/-! # (x) ⟺ (xi): Complementation -/
 
 private lemma x_iff_xi : stmt_x f ↔ stmt_xi f := by
   constructor
@@ -841,7 +843,7 @@ private lemma x_iff_xi : stmt_x f ↔ stmt_xi f := by
     rw [h_eq]
     exact (hxi _ hU.isClosed_compl).complement
 
-/-! ### (x) ⟹ (vii): {f < λ} = f⁻¹'(Iio λ) and Iio λ is open -/
+/-! # (x) ⟹ (vii): \{f < λ\} = f⁻¹'({name}`Set.Iio` λ) and {name}`Set.Iio` λ is open -/
 
 private lemma x_imp_vii : stmt_x f → stmt_vii f := by
   intro hx t
@@ -850,7 +852,7 @@ private lemma x_imp_vii : stmt_x f → stmt_vii f := by
   rw [h_eq]
   exact hx _ h_open
 
-/-! ### (v)-(xi) ⟹ (iv): Construction of approximating sequence -/
+/-! # (v)-(xi) ⟹ (iv): Construction of approximating sequence -/
 
 -- Helper: the norm ball centered at origin is Lebesgue measurable
 private lemma normBall_LebesgueMeasurable (r : ℝ) :
@@ -1755,27 +1757,27 @@ theorem UnsignedMeasurable.measurable_graph {d:ℕ} {f: EuclideanSpace' d → ER
 /-!
 ## Remark 1.3.10: Measurable functions can have non-measurable preimages
 
-We construct an example showing that even for a measurable function f: ℝ^d → [0, +∞],
+We construct an example showing that even for a measurable function f: ℝ^d → \[0, +∞\],
 the inverse image f⁻¹(E) of a Lebesgue measurable set E need not be Lebesgue measurable.
 
 **Strategy** (from the textbook):
-1. The Cantor set C := {∑ aⱼ 3^{-j} : aⱼ ∈ {0,2}} has measure zero
-2. Define f: [0,1] → C by mapping binary digits to ternary: f(∑ bⱼ 2^{-j}) = ∑ 2bⱼ 3^{-j}
+1. The Cantor set C := \{∑ aⱼ 3^(-j) : aⱼ ∈ \{0,2\}\} has measure zero
+2. Define f: \[0,1\] → C by mapping binary digits to ternary: f(∑ bⱼ 2^(-j)) = ∑ 2bⱼ 3^(-j)
 3. f is bijective from A (non-terminating binary decimals) onto C, and f is measurable
 4. Take non-measurable F ⊆ A (from Vitali construction)
 5. E := f(F) ⊆ C is measurable (subset of null set), but f⁻¹(E) = F is non-measurable
 
 **Implementation note**: Our formalization differs slightly from the textbook:
 - **Textbook**: f(x) = 0 for dyadic rationals (terminating binary decimals)
-- **Our version**: f is defined uniformly for all x ∈ [0,1] using floor-based binary digits
+- **Our version**: f is defined uniformly for all x ∈ \[0,1\] using floor-based binary digits
 
-The textbook's f is NOT monotone on [0,1] (e.g., f(0.4) > 0 but f(0.5) = 0).
-Our f IS monotone on all of [0,1], which simplifies the measurability proof:
+The textbook's f is NOT monotone on \[0,1\] (e.g., f(0.4) > 0 but f(0.5) = 0).
+Our f IS monotone on all of \[0,1\], which simplifies the measurability proof:
 sublevel sets are intervals, hence measurable by Lemma 1.3.9(viii).
 
 Both versions work for the theorem because:
 - Both are injective on A (non-dyadic numbers have unique binary expansions)
-- Both map [0,1] into CantorSet ∪ {0}
+- Both map \[0,1\] into {name}`CantorSet` ∪ \{0\}
 - Both give measurable f with f⁻¹(E) = F non-measurable
 -/
 
@@ -1796,15 +1798,15 @@ lemma DyadicRationals.countable : DyadicRationals.Countable := by
   exact ⟨⟨k, hk_lt⟩, hk.symm⟩
 
 /-- Binary digit extraction: bⱼ(x) = ⌊2^j · x⌋ mod 2.
-    For x ∈ [0,1), this extracts the j-th binary digit.
+    For x ∈ \[0,1), this extracts the j-th binary digit.
     Special case: x = 1 has all digits = 1 (1 = 0.111...₂).
-    For x ∉ [0,1], all digits are 0. -/
+    For x ∉ \[0,1\], all digits are 0. -/
 noncomputable def binaryDigit (x : ℝ) (j : ℕ) : ℕ :=
   if x ∈ Set.Ico (0:ℝ) 1 then ⌊(2:ℝ)^j * x⌋₊ % 2
   else if x = 1 then 1
   else 0
 
-/-- Binary digits are in {0, 1}. -/
+/-- Binary digits are in \{0, 1\}. -/
 lemma binaryDigit_le_one (x : ℝ) (j : ℕ) : binaryDigit x j ≤ 1 := by
   simp only [binaryDigit]
   split_ifs with h1 h2 <;> omega
@@ -1820,7 +1822,7 @@ lemma binaryDigit_zero (j : ℕ) : binaryDigit 0 j = 0 := by
 lemma binaryDigit_one (j : ℕ) : binaryDigit 1 j = 1 := by
   simp only [binaryDigit, Set.mem_Ico, lt_self_iff_false, and_false, ↓reduceIte]
 
-/-- The full sum ∑_{j≥0} 2·(1/3)^{j+1} = 1. -/
+/-- The full sum ∑\_\{j≥0\} 2·(1/3)^(j+1) = 1. -/
 lemma tsum_two_thirds_geometric : ∑' j : ℕ, (2:ℝ) * (1/3:ℝ)^(j + 1) = 1 := by
   have h1 : ∑' j : ℕ, (1/3:ℝ)^j = (1 - 1/3)⁻¹ :=
     tsum_geometric_of_lt_one (by norm_num) (by norm_num)
@@ -1830,7 +1832,7 @@ lemma tsum_two_thirds_geometric : ∑' j : ℕ, (2:ℝ) * (1/3:ℝ)^(j + 1) = 1
     _ = (2/3) * (1 - 1/3)⁻¹ := by rw [h1]
     _ = 1 := by norm_num
 
-/-- The tail sum bound: ∑_{j≥k} 2·(1/3)^{j+1} = (1/3)^k. -/
+/-- The tail sum bound: ∑\_\{j≥k\} 2·(1/3)^(j+1) = (1/3)^k. -/
 lemma tsum_tail_bound (k : ℕ) :
     ∑' j : ℕ, (2:ℝ) * (1/3:ℝ)^(k + j + 1) = (1/3:ℝ)^k := by
   have h1 : ∑' j : ℕ, (1/3:ℝ)^j = (1 - 1/3)⁻¹ :=
@@ -1918,10 +1920,10 @@ lemma floor_two_mul_eq_of_mod_eq {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y)
 namespace Remark_1_3_10
 
 /-- The properties required of the binary-to-ternary function for this construction.
-    The function maps [0,1] into the Cantor set C by converting binary digits to ternary.
+    The function maps \[0,1\] into the Cantor set C by converting binary digits to ternary.
 
     Note: Unlike the textbook (which sets g(x) = 0 for dyadic rationals), our g is defined
-    uniformly for all x ∈ [0,1]. This makes g monotone on ALL of [0,1], not just on A. -/
+    uniformly for all x ∈ \[0,1\]. This makes g monotone on ALL of \[0,1\], not just on A. -/
 structure BinaryToTernaryProperties (g : ℝ → ℝ) : Prop where
   nonneg : ∀ x, 0 ≤ g x
   bounded : ∀ x, g x ≤ 1
@@ -1935,13 +1937,13 @@ structure BinaryToTernaryProperties (g : ℝ → ℝ) : Prop where
     Set.InjOn g A ∧                 -- g is injective on A (hence bijective onto g(A) ⊆ C)
     A ∩ DyadicRationals = ∅         -- A excludes dyadic rationals
 
-/-- The binary-to-ternary function: g(x) = ∑_{j≥1} 2·bⱼ(x)·3^{-j} for x ∈ [0,1], else 0. -/
+/-- The binary-to-ternary function: g(x) = ∑\_\{j≥1\} 2·bⱼ(x)·3^(-j) for x ∈ \[0,1\], else 0. -/
 noncomputable def binaryToTernaryFn (x : ℝ) : ℝ :=
   if x ∈ Set.Icc (0:ℝ) 1 then
     ∑' j : ℕ, (2 * binaryDigit x (j + 1) : ℝ) * (1/3:ℝ)^(j + 1)
   else 0
 
-/-- The series ∑ 2·bⱼ(x)·3^{-j} is summable for any x. -/
+/-- The series ∑ 2·bⱼ(x)·3^(-j) is summable for any x. -/
 lemma binaryToTernary_summable (x : ℝ) :
     Summable (fun j => (2 * binaryDigit x (j + 1) : ℝ) * (1/3:ℝ)^(j + 1)) := by
   apply Summable.of_nonneg_of_le
@@ -1957,7 +1959,7 @@ lemma binaryToTernary_summable (x : ℝ) :
   · have h : Summable (fun j : ℕ => (1/3:ℝ)^j) := summable_geometric_of_lt_one (by norm_num) (by norm_num)
     exact (h.mul_left 2).comp_injective (fun _ _ h => Nat.succ_injective h)
 
-/-! ### Helper lemmas for monotonicity proof -/
+/-! # Helper lemmas for monotonicity proof -/
 
 /-- For x ∈ (0, 1), there exists a position where the binary digit is 1. -/
 lemma binaryDigit_exists_one_of_pos {x : ℝ} (hx_pos : 0 < x) (hx_lt : x < 1) :
@@ -2001,7 +2003,7 @@ lemma binaryDigit_partial_sum_le {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (n : 
   rw [div_le_iff₀ h2n_pos, mul_comm]
   exact Nat.floor_le (mul_nonneg hx.1 (le_of_lt h2n_pos))
 
-/-- The partial sum bounds x from above: x < Sₙ(x) + 2^{-n} -/
+/-- The partial sum bounds x from above: x < Sₙ(x) + 2^(-n) -/
 lemma binaryDigit_partial_sum_lt (x : ℝ) (n : ℕ) :
     x < (⌊(2:ℝ)^n * x⌋₊ : ℝ) / (2:ℝ)^n + (1:ℝ) / (2:ℝ)^n := by
   have h2n_pos : (0:ℝ) < 2^n := by positivity
@@ -2012,7 +2014,7 @@ lemma binaryDigit_partial_sum_lt (x : ℝ) (n : ℕ) :
         apply div_lt_div_of_pos_right h1 h2n_pos
     _ = (⌊(2:ℝ)^n * x⌋₊ : ℝ) / (2:ℝ)^n + (1:ℝ) / (2:ℝ)^n := by ring
 
-/-- Key lemma: if bₖ(x) = 1, then x ≥ ⌊2^k * x⌋₊ / 2^k + 2^{-(k+1)} -/
+/-- Key lemma: if bₖ(x) = 1, then `x ≥ floor(2^k * x) / 2^k + 2^(-(k+1))` -/
 lemma binaryDigit_one_implies_lower_bound {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (k : ℕ)
     (hbk : binaryDigit x (k + 1) = 1) :
     (⌊(2:ℝ)^k * x⌋₊ : ℝ) / (2:ℝ)^k + (1:ℝ) / (2:ℝ)^(k + 1) ≤ x := by
@@ -2032,7 +2034,7 @@ lemma binaryDigit_one_implies_lower_bound {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ)
         exact_mod_cast h_floor_rel
     _ ≤ x := binaryDigit_partial_sum_le hx (k + 1)
 
-/-- Key lemma: if bₖ(y) = 0, then y < ⌊2^k * y⌋₊ / 2^k + 2^{-(k+1)} -/
+/-- Key lemma: if bₖ(y) = 0, then `y < floor(2^k * y) / 2^k + 2^(-(k+1))` -/
 lemma binaryDigit_zero_implies_upper_bound {y : ℝ} (hy : y ∈ Set.Ico (0:ℝ) 1) (k : ℕ)
     (hbk : binaryDigit y (k + 1) = 0) :
     y < (⌊(2:ℝ)^k * y⌋₊ : ℝ) / (2:ℝ)^k + (1:ℝ) / (2:ℝ)^(k + 1) := by
@@ -2055,7 +2057,7 @@ lemma binaryDigit_zero_implies_upper_bound {y : ℝ} (hy : y ∈ Set.Ico (0:ℝ)
         linarith
     _ = (⌊(2:ℝ)^k * y⌋₊ : ℝ) / (2:ℝ)^k + (1:ℝ) / (2:ℝ)^(k + 1) := by field_simp; ring
 
-/-- Helper: floors of x, y in [0,1) are equal up to level n if their binary digits agree up to level n-1. -/
+/-- Helper: floors of x, y in \[0,1) are equal up to level n if their binary digits agree up to level n-1. -/
 lemma floor_eq_of_binaryDigit_eq {x y : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (hy : y ∈ Set.Ico (0:ℝ) 1)
     (heq : ∀ j < n, binaryDigit x (j + 1) = binaryDigit y (j + 1)) :
     ⌊(2:ℝ)^n * x⌋₊ = ⌊(2:ℝ)^n * y⌋₊ := by
@@ -2079,7 +2081,7 @@ lemma floor_eq_of_binaryDigit_eq {x y : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (hy
     rw [h1, h2]
     exact floor_two_mul_eq_of_mod_eq hx_nonneg hy_nonneg ih' hmod_eq'
 
-/-- For x, y ∈ [0,1) with x < y, there exists a first position k where bₖ(x) < bₖ(y). -/
+/-- For x, y ∈ \[0,1) with x < y, there exists a first position k where bₖ(x) < bₖ(y). -/
 lemma binaryDigit_first_diff {x y : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (hy : y ∈ Set.Ico (0:ℝ) 1)
     (hxy : x < y) :
     ∃ k, binaryDigit x (k + 1) < binaryDigit y (k + 1) ∧
@@ -2194,9 +2196,9 @@ lemma binaryToTernary_lt_of_digit_lt {x y : ℝ}
   have h3pos : (0:ℝ) < (1/3)^(k + 1) := by positivity
   linarith
 
-/-! ### Helper lemmas for injectivity proof -/
+/-! # Helper lemmas for injectivity proof -/
 
-/-- Ternary {0,2} expansions are unique. -/
+/-- Ternary \{0,2\} expansions are unique. -/
 lemma ternary_02_expansion_unique {d e : ℕ → ℕ}
     (hd : ∀ j, d j ∈ ({0, 2} : Set ℕ))
     (he : ∀ j, e j ∈ ({0, 2} : Set ℕ))
@@ -2311,7 +2313,7 @@ lemma ternary_02_expansion_unique {d e : ℕ → ℕ}
     linarith
   · omega
 
-/-! ### Helper lemmas for binary expansion sums -/
+/-! # Helper lemmas for binary expansion sums -/
 
 /-- ⌊2y⌋ = 2⌊y⌋ + ⌊2y⌋ % 2 for y ≥ 0. -/
 private lemma floor_two_mul_decomp {y : ℝ} (_hy : 0 ≤ y) :
@@ -2320,7 +2322,7 @@ private lemma floor_two_mul_decomp {y : ℝ} (_hy : 0 ≤ y) :
   have h_div : ⌊2 * y⌋₊ / 2 = ⌊y⌋₊ := Nat.cast_mul_floor_div_cancel (by norm_num : (2:ℕ) ≠ 0) y
   omega
 
-/-- Partial sum identity: ∑_{j < n} b_j * 2^{-(j+1)} = ⌊2^n * x⌋ / 2^n. -/
+/-- Partial sum identity: `∑ (j < n) bⱼ * 2^(-(j+1)) = floor(2^n * x) / 2^n`. -/
 private lemma partial_sum_eq_floor {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (n : ℕ) :
     ∑ j ∈ Finset.range n, (binaryDigit x (j + 1) : ℝ) * (1/2:ℝ)^(j + 1) =
     (⌊(2:ℝ)^n * x⌋₊ : ℝ) / (2:ℝ)^n := by
@@ -2355,7 +2357,7 @@ private lemma partial_sum_eq_floor {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (n :
     rw [h_floor']
     field_simp
 
-/-- Binary series is summable for x ∈ [0,1). -/
+/-- Binary series is summable for x ∈ \[0,1). -/
 private lemma binary_summable {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) :
     Summable (fun j => (binaryDigit x (j + 1) : ℝ) * (1/2:ℝ)^(j + 1)) := by
   apply Summable.of_nonneg_of_le
@@ -2372,7 +2374,7 @@ private lemma binary_summable {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) :
   · have h : Summable (fun j : ℕ => (1/2:ℝ)^j) := summable_geometric_of_lt_one (by norm_num) (by norm_num)
     exact h.comp_injective (fun _ _ h => Nat.succ_injective h)
 
-/-- For non-dyadic x ∈ [0,1), x equals its binary expansion sum. -/
+/-- For non-dyadic x ∈ \[0,1), x equals its binary expansion sum. -/
 lemma non_dyadic_eq_binary_sum {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (_hnd : x ∉ DyadicRationals) :
     x = ∑' j : ℕ, (binaryDigit x (j + 1) : ℝ) * (1/2:ℝ)^(j + 1) := by
   have h_summable := binary_summable hx
@@ -2418,7 +2420,7 @@ lemma non_dyadic_eq_binary_sum {x : ℝ} (hx : x ∈ Set.Ico (0:ℝ) 1) (_hnd :
     exact h_floor_to_x
   exact tendsto_nhds_unique h_partial_to_x h_partial_to_tsum
 
-/-- Non-dyadic x ∈ [0,1) with equal binary digits are equal. -/
+/-- Non-dyadic x ∈ \[0,1) with equal binary digits are equal. -/
 lemma eq_of_binaryDigit_eq_of_non_dyadic {x₁ x₂ : ℝ}
     (hx₁ : x₁ ∈ Set.Ico (0:ℝ) 1) (hx₂ : x₂ ∈ Set.Ico (0:ℝ) 1)
     (hnd₁ : x₁ ∉ DyadicRationals) (hnd₂ : x₂ ∉ DyadicRationals)
@@ -2431,9 +2433,9 @@ lemma eq_of_binaryDigit_eq_of_non_dyadic {x₁ x₂ : ℝ}
   ext j
   rw [heq (j + 1)]
 
-/-! ### Helper lemmas for image_in_cantor -/
+/-! # Helper lemmas for image_in_cantor -/
 
-/-- Points with {0,2} ternary digits are in the Cantor set. -/
+/-- Points with \{0,2\} ternary digits are in the Cantor set. -/
 lemma mem_CantorSet_of_ternary_02 {y : ℝ} (d : ℕ → ℕ)
     (hd : ∀ j, d j ∈ ({0, 2} : Set ℕ))
     (hsum : Summable (fun j => (d j : ℝ) * (1/3:ℝ)^(j + 1)))
@@ -2496,7 +2498,7 @@ lemma mem_CantorSet_of_ternary_02 {y : ℝ} (d : ℕ → ℕ)
   · rw [← h_one_third_pow]
     exact add_le_add_right h_tail_bound _
 
-/-- Existence of a binary-to-ternary function: g(x) = ∑ 2bⱼ 3^{-j}. -/
+/-- Existence of a binary-to-ternary function: g(x) = ∑ 2bⱼ 3^(-j). -/
 lemma binaryToTernary_exists : ∃ g : ℝ → ℝ, BinaryToTernaryProperties g := by
   use binaryToTernaryFn
   exact {
@@ -2690,13 +2692,13 @@ lemma binaryToTernary_exists : ∃ g : ℝ → ℝ, BinaryToTernaryProperties g
         exact hx_not_dyadic hx_dyadic
   }
 
-/-- Binary-to-ternary function: g(x) = ∑ 2·bⱼ(x)·3^{-j}, monotone on [0,1], g([0,1]) ⊆ C ∪ {0}. -/
+/-- Binary-to-ternary function: g(x) = ∑ 2·bⱼ(x)·3^(-j), monotone on \[0,1\], g(\[0,1\]) ⊆ C ∪ \{0\}. -/
 noncomputable def binaryToTernary : ℝ → ℝ := Classical.choose binaryToTernary_exists
 
 lemma binaryToTernary_props : BinaryToTernaryProperties binaryToTernary :=
   Classical.choose_spec binaryToTernary_exists
 
-/-- binaryToTernary x = 0 iff x = 0 for x ∈ [0,1]. -/
+/-- {lean}`binaryToTernary x = 0` iff {lean}`x = 0` for x ∈ \[0,1\]. -/
 lemma binaryToTernary_eq_zero_iff {x : ℝ} (hx : x ∈ Set.Icc (0:ℝ) 1) :
     binaryToTernary x = 0 ↔ x = 0 := by
   constructor
@@ -2730,7 +2732,7 @@ lemma binaryToTernary_eq_zero_iff {x : ℝ} (hx : x ∈ Set.Icc (0:ℝ) 1) :
     rw [h]
     exact binaryToTernary_props.zero_at_zero
 
-/-- binaryToTernary lifted to EuclideanSpace' 1 → EReal (called f in informal proof). -/
+/-- {name}`binaryToTernary` lifted to {lean}`EuclideanSpace' 1 → EReal` (called f in informal proof). -/
 noncomputable def f_lifted : EuclideanSpace' 1 → EReal :=
   fun x => Real.toEReal (max 0 (binaryToTernary (EuclideanSpace'.equiv_Real x)))
 
@@ -2824,7 +2826,7 @@ lemma f_lifted_zero_set_measurable : LebesgueMeasurable {x : EuclideanSpace' 1 |
       apply Set.Countable.image; exact f_zero_set_in_interval_countable
     exact Countable.Lebesgue_measure Nat.one_pos h_countable
 
-/-- Sublevel sets of f_lifted are measurable (key lemma for f_lifted_measurable). -/
+/-- Sublevel sets of {name}`f_lifted` are measurable (key lemma for `f_lifted_measurable`). -/
 lemma sublevel_set_measurable (t : EReal) (ht_pos : 0 < t) (ht_lt_one : t < 1) :
     LebesgueMeasurable {x : EuclideanSpace' 1 | f_lifted x ≤ t} := by
   have h_outside_zero : ∀ x : EuclideanSpace' 1, EuclideanSpace'.equiv_Real x ∉ Set.Icc 0 1 →
@@ -3023,7 +3025,7 @@ lemma f_lifted_measurable : UnsignedMeasurable f_lifted := by
       rw [h_univ]; exact IsOpen.measurable isOpen_univ
     · exact sublevel_set_measurable t ht_pos ht_lt_one
 
-/-- Non-measurable F ⊆ [0,1] with binaryToTernary(F) ⊆ Cantor set (Vitali construction). -/
+/-- Non-measurable F ⊆ \[0,1\] with {name}`binaryToTernary`(F) ⊆ Cantor set (Vitali construction). -/
 lemma exists_nonmeasurable_with_cantor_image :
     ∃ F : Set ℝ, ∃ A : Set ℝ, F ⊆ Set.Icc 0 1 ∧
     ¬ LebesgueMeasurable (Real.equiv_EuclideanSpace' '' F) ∧
@@ -3094,7 +3096,7 @@ end Remark_1_3_10
 
 /-- Remark 1.3.10: The inverse image of a Lebesgue measurable set by a measurable function
     need not be Lebesgue measurable.
-    Proof: Let f = binaryToTernary (maps [0,1] → Cantor set), F ⊆ [0,1] non-measurable (Vitali).
+    Proof: Let f = {name}`Remark_1_3_10.binaryToTernary` (maps \[0,1\] → Cantor set), F ⊆ \[0,1\] non-measurable (Vitali).
     Set E = f(F) ⊆ Cantor set. Then E is null (⊆ null set) hence measurable, but f⁻¹(E) = F
     is non-measurable. (Uses injectivity of f on non-dyadic rationals A ⊇ F.) -/
 example : ∃ (f: EuclideanSpace' 1 → EReal) (_hf: UnsignedMeasurable f) (E: Set (EuclideanSpace' 1)) (_hE: LebesgueMeasurable E), ¬ LebesgueMeasurable (f⁻¹' ((Real.toEReal ∘ EuclideanSpace'.equiv_Real) '' E)) := by
diff --git a/analysis/Analysis/MeasureTheory/Section_1_3_3.lean b/Analysis/MeasureTheory/Section_1_3_3.lean
similarity index 99%
rename from analysis/Analysis/MeasureTheory/Section_1_3_3.lean
rename to Analysis/MeasureTheory/Section_1_3_3.lean
index 11175f8b..f2d1df87 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_3_3.lean
+++ b/Analysis/MeasureTheory/Section_1_3_3.lean
@@ -220,7 +220,7 @@ lemma FiniteMeasureSupport.mul_indicator_ball {d : ℕ} {f : EuclideanSpace' d 
   sorry
 
 /-- Additivity of lower integral for finite-support functions.
-    This is the key step where we can apply eq_upperIntegral and use the sandwich argument. -/
+    This is the key step where we can apply {name}`eq_upperIntegral` and use the sandwich argument. -/
 lemma LowerUnsignedLebesgueIntegral.add_of_finiteSupport {d : ℕ}
     {f g : EuclideanSpace' d → EReal}
     (hf : UnsignedMeasurable f) (hg : UnsignedMeasurable g)
diff --git a/analysis/Analysis/MeasureTheory/Section_1_3_4.lean b/Analysis/MeasureTheory/Section_1_3_4.lean
similarity index 100%
rename from analysis/Analysis/MeasureTheory/Section_1_3_4.lean
rename to Analysis/MeasureTheory/Section_1_3_4.lean
diff --git a/analysis/Analysis/MeasureTheory/Section_1_3_5.lean b/Analysis/MeasureTheory/Section_1_3_5.lean
similarity index 100%
rename from analysis/Analysis/MeasureTheory/Section_1_3_5.lean
rename to Analysis/MeasureTheory/Section_1_3_5.lean
diff --git a/analysis/Analysis/MeasureTheory/Section_1_4_1.lean b/Analysis/MeasureTheory/Section_1_4_1.lean
similarity index 98%
rename from analysis/Analysis/MeasureTheory/Section_1_4_1.lean
rename to Analysis/MeasureTheory/Section_1_4_1.lean
index 3f0cb4c8..14a21d9c 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_4_1.lean
+++ b/Analysis/MeasureTheory/Section_1_4_1.lean
@@ -114,7 +114,7 @@ def ConcreteBooleanAlgebra.restrict_iff {X:Type*} {B: ConcreteBooleanAlgebra X}
   (B.restrict A).measurable E ↔ B.measurable A :=
   by sorry
 
-/-- Remark 1.4.2: ConcreteBooleanAlgebras are BooleanAlgebras -/
+/-- Remark 1.4.2: {name}`ConcreteBooleanAlgebra`s are {name}`BooleanAlgebra`s -/
 def ConcreteBooleanAlgebra.toBooleanAlgebra {X:Type*} (B: ConcreteBooleanAlgebra X) : BooleanAlgebra (B.measurableSets) :=
 {
    sup := sorry
@@ -172,7 +172,7 @@ def IsPartition.remove_empty_to_ConcreteBooleanAlgebra {I X:Type*} {parts: I →
   h_part.remove_empty.to_ConcreteBooleanAlgebra :=
   by sorry
 
-/-- A variant of DyadicCube with Ico intervals -/
+/-- A variant of {name}`DyadicCube` with {name}`BoundedInterval.Ico` intervals -/
 noncomputable def DyadicCube' {d:ℕ} (n:ℤ) (a: Fin d → ℤ) : Box d := { side := fun i ↦ BoundedInterval.Ico (a i/2^n) ((a i + 1)/2^n) }
 
 /-- Example 1.4.8 -/
diff --git a/analysis/Analysis/MeasureTheory/Section_1_4_2.lean b/Analysis/MeasureTheory/Section_1_4_2.lean
similarity index 100%
rename from analysis/Analysis/MeasureTheory/Section_1_4_2.lean
rename to Analysis/MeasureTheory/Section_1_4_2.lean
diff --git a/analysis/Analysis/MeasureTheory/Section_1_4_3.lean b/Analysis/MeasureTheory/Section_1_4_3.lean
similarity index 98%
rename from analysis/Analysis/MeasureTheory/Section_1_4_3.lean
rename to Analysis/MeasureTheory/Section_1_4_3.lean
index 33909559..aa87d59a 100644
--- a/analysis/Analysis/MeasureTheory/Section_1_4_3.lean
+++ b/Analysis/MeasureTheory/Section_1_4_3.lean
@@ -5,7 +5,7 @@ import Analysis.MeasureTheory.Section_1_4_2
 
 A companion to (the introduction to) Section 1.4.3 of the book "An introduction to Measure Theory".
 
-Note: initially this section will use custom-notions of concrete sigma algebras and countably additive measures, but will transition to the Mathlib notions of `Measurable` and `Measure`, which will be in use going forward.  In particular, exercises past this point will be easier
+Note: initially this section will use custom-notions of concrete sigma algebras and countably additive measures, but will transition to the Mathlib notions of {name}`Measurable` and {name}`MeasureTheory.Measure`, which will be in use going forward. In particular, exercises past this point will be easier
 to solve using the Mathlib library for measure theory than the custom results defined here.
 -/
 
diff --git a/analysis/Analysis/MeasureTheory/Section_1_4_4.lean b/Analysis/MeasureTheory/Section_1_4_4.lean
similarity index 100%
rename from analysis/Analysis/MeasureTheory/Section_1_4_4.lean
rename to Analysis/MeasureTheory/Section_1_4_4.lean
diff --git a/analysis/Analysis/MeasureTheory/Section_1_4_5.lean b/Analysis/MeasureTheory/Section_1_4_5.lean
similarity index 100%
rename from analysis/Analysis/MeasureTheory/Section_1_4_5.lean
rename to Analysis/MeasureTheory/Section_1_4_5.lean
diff --git a/analysis/Analysis/Misc/Combinatorics.lean b/Analysis/Misc/Combinatorics.lean
similarity index 97%
rename from analysis/Analysis/Misc/Combinatorics.lean
rename to Analysis/Misc/Combinatorics.lean
index f343e167..ffed38ea 100644
--- a/analysis/Analysis/Misc/Combinatorics.lean
+++ b/Analysis/Misc/Combinatorics.lean
@@ -7,7 +7,7 @@ General combinatorics lemmas about Fin, Finset, and boolean choices.
 -/
 
 /-- Distributive law: product of sums over Fin d equals sum over boolean choices of products.
-    This is the key identity: ∏ᵢ (aᵢ + bᵢ) = ∑_{c : Fin d → Bool} ∏ᵢ (if cᵢ then bᵢ else aᵢ) -/
+    This is the key identity: ∏ᵢ (aᵢ + bᵢ) = ∑\_\{c : Fin d → Bool\} ∏ᵢ (if cᵢ then bᵢ else aᵢ) -/
 lemma Fin.prod_add_eq_sum_prod_choice (d : ℕ) (a b : Fin d → ℝ) :
     ∏ i, (a i + b i) = ∑ c : Fin d → Bool, ∏ i, (if c i then b i else a i) := by
   induction d with
diff --git a/analysis/Analysis/Misc/FiniteChoice.lean b/Analysis/Misc/FiniteChoice.lean
similarity index 92%
rename from analysis/Analysis/Misc/FiniteChoice.lean
rename to Analysis/Misc/FiniteChoice.lean
index cd48cc42..d8558297 100644
--- a/analysis/Analysis/Misc/FiniteChoice.lean
+++ b/Analysis/Misc/FiniteChoice.lean
@@ -32,7 +32,7 @@ lemma sec_ex {α β:Type*} [Fintype β] [DecidableEq β] (f : α → β) (h : 
   ext b; specialize hg (e b)
   simpa only [Function.comp_apply, id_eq, Fin.val_inj, EmbeddingLike.apply_eq_iff_eq, F] using hg
 
-/-- Variants of the above that use `Trunc` in place of `∃`.  Roughly speaking, this means that if the hypotheses are constructive, we can guarantee that the conclusion is constructive -/
+/-- Variants of the above that use {name}`Trunc` in place of {kw (of := Lean.«term∃__,_»)}`∃`.  Roughly speaking, this means that if the hypotheses are constructive, we can guarantee that the conclusion is constructive. -/
 
 def finite_choice_trunc {X:Type*} {f:X → ℕ} {N:ℕ} (h: ∀ n < N, Trunc {x // f x = n}) :
   Trunc {g: Fin N → X // ∀ n, f (g n) = n} := by
diff --git a/analysis/Analysis/Misc/NatBitwise.lean b/Analysis/Misc/NatBitwise.lean
similarity index 75%
rename from analysis/Analysis/Misc/NatBitwise.lean
rename to Analysis/Misc/NatBitwise.lean
index eedefe56..333e6739 100644
--- a/analysis/Analysis/Misc/NatBitwise.lean
+++ b/Analysis/Misc/NatBitwise.lean
@@ -4,15 +4,15 @@ import Mathlib.Combinatorics.Colex
 /-!
 # Additional lemmas for natural number bit operations
 
-This file contains general-purpose lemmas about `Nat.testBit`, `Nat.bitIndices`,
+This file contains general-purpose lemmas about {name}`Nat.testBit`, {name}`Nat.bitIndices`,
 and sums of powers of 2 that are used throughout the formalization.
 
 ## Main results
 
-* `Nat.testBit_iff_mem_bitIndices`: `n.testBit i = true ↔ i ∈ n.bitIndices`
-* `Nat.testBit_finset_sum_pow_two`: For a finset `s` of natural numbers,
-  `(∑ i ∈ s, 2^i).testBit j ↔ j ∈ s`
-* `Nat.testBit_sum_pow_two_fin`: Same for `Finset (Fin k)`
+* {given -show}`n : ℕ, i : ℕ` `Nat.testBit_iff_mem_bitIndices`: {lean}`n.testBit i = true ↔ i ∈ n.bitIndices`
+* {given -show}`j` `Nat.testBit_finset_sum_pow_two`: For a finset {given}`s` of natural numbers,
+  {lean}`(∑ i ∈ s, 2^i).testBit j ↔ j ∈ s`
+* {given -show}`k` `Nat.testBit_sum_pow_two_fin`: Same for {lean}`Finset (Fin k)`
 
 These lemmas connect the bit representation of natural numbers with finset membership,
 which is fundamental for binary encoding arguments.
@@ -20,7 +20,7 @@ which is fundamental for binary encoding arguments.
 
 namespace Nat
 
-/-- `n.testBit i = true` if and only if `i` appears in `n.bitIndices`.
+/-- {lean}`n.testBit i = true` if and only if {name}`i` appears in {lean}`n.bitIndices`.
     This connects the pointwise bit test with the list of set bit positions. -/
 lemma testBit_iff_mem_bitIndices (n i : ℕ) :
     n.testBit i = true ↔ i ∈ n.bitIndices := by
@@ -58,8 +58,9 @@ lemma testBit_iff_mem_bitIndices (n i : ℕ) :
         · rw [Nat.testBit_bit_succ]
           exact ih _ hj
 
-/-- `testBit` of a sum of distinct powers of 2 equals membership in the index set.
-    For a finset `s` of natural numbers, `(∑ i ∈ s, 2^i).testBit j = true ↔ j ∈ s`. -/
+/-- {name}`Nat.testBit` of a sum of distinct powers of 2 equals membership in the index set.
+    For a finset {name}`s` of natural numbers,
+    {given -show}`j` {lean}`(∑ i ∈ s, 2^i).testBit j = true ↔ j ∈ s`. -/
 lemma testBit_finset_sum_pow_two {s : Finset ℕ} {i : ℕ} :
     (s.sum (2^·)).testBit i = true ↔ i ∈ s := by
   rw [testBit_iff_mem_bitIndices]
@@ -74,8 +75,8 @@ lemma testBit_finset_sum_pow_two {s : Finset ℕ} {i : ℕ} :
       exact h
     exact List.mem_toFinset.mp this
 
-/-- `testBit` of a sum of `2^j` over `Finset (Fin k)` equals membership.
-    This is the `Fin`-indexed version of `testBit_finset_sum_pow_two`. -/
+/-- {name}`Nat.testBit` of a sum of {lean (type := "ℕ")}`2^j.val` over {lean}`Finset (Fin k)` equals membership.
+    This is the {name}`Fin`-indexed version of {name}`Nat.testBit_finset_sum_pow_two`. -/
 lemma testBit_sum_pow_two_fin {k : ℕ} {s : Finset (Fin k)} (j : Fin k) :
     (s.sum fun i => (2:ℕ)^i.val).testBit j.val ↔ j ∈ s := by
   have h : s.sum (fun i => (2:ℕ)^i.val) = (s.image (·.val)).sum (2^·) := by
diff --git a/analysis/Analysis/Misc/Probability.lean b/Analysis/Misc/Probability.lean
similarity index 100%
rename from analysis/Analysis/Misc/Probability.lean
rename to Analysis/Misc/Probability.lean
diff --git a/analysis/Analysis/Misc/Real-EReal-ENNReal.lean b/Analysis/Misc/Real-EReal-ENNReal.lean
similarity index 93%
rename from analysis/Analysis/Misc/Real-EReal-ENNReal.lean
rename to Analysis/Misc/Real-EReal-ENNReal.lean
index 4e442ea1..6b3a28dc 100644
--- a/analysis/Analysis/Misc/Real-EReal-ENNReal.lean
+++ b/Analysis/Misc/Real-EReal-ENNReal.lean
@@ -3,7 +3,7 @@ import Mathlib.Tactic
 /-!
 # General utilities for Real, EReal, and ENNReal
 
-This file contains general-purpose lemmas about Real, EReal, and ENNReal
+This file contains general-purpose lemmas about {name}`Real`, {name}`EReal`, and {name}`ENNReal`
 that are not specific to measure theory but are used throughout the formalization.
 -/
 
@@ -18,8 +18,8 @@ lemma max_div_two (x : ℝ) : max x 0 / 2 = max (x / 2) 0 := by
   · push_neg at hx
     simp [max_eq_right (le_of_lt hx), max_eq_right (by linarith : x / 2 ≤ 0)]
 
-/-- The square root function is subadditive: √(x + y) ≤ √x + √y for non-negative reals.
-    This follows from the fact that (√x + √y)² = x + y + 2√(xy) ≥ x + y. -/
+/-- The square root function is subadditive: {lean}`√(x + y) ≤ √x + √y` for non-negative reals.
+    This follows from the fact that `(√x + √y)² = x + y + 2√(xy) ≥ x + y`. -/
 lemma Real.sqrt_add_le_add_sqrt {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) :
     √(x + y) ≤ √x + √y := by
   by_cases hxy : x + y = 0
@@ -39,7 +39,7 @@ lemma Real.sqrt_add_le_add_sqrt {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) :
         _ = (√x + √y) ^ 2 := by ring
     exact this
 
-/-- The square root function is subadditive over finite sums: √(∑ᵢ xᵢ) ≤ ∑ᵢ √xᵢ
+/-- The square root function is subadditive over finite sums: `√(∑ᵢ xᵢ) ≤ ∑ᵢ √xᵢ`
     for non-negative terms. This is a consequence of the concavity of sqrt. -/
 lemma Real.sqrt_sum_le_sum_sqrt {ι : Type*} [Fintype ι] [DecidableEq ι] (f : ι → ℝ)
     (hf : ∀ i, 0 ≤ f i) :
@@ -63,14 +63,14 @@ lemma Real.sqrt_sum_le_sum_sqrt {ι : Type*} [Fintype ι] [DecidableEq ι] (f :
 -- EReal utilities
 -- =============================================================================
 
-/-- For EReal, adding a positive real value to a value that is neither ⊥ nor ⊤ gives a strictly greater result. -/
+/-- For {name}`EReal`, adding a positive real value to a value that is neither {lean (type := "EReal")}`⊥` nor {lean (type := "EReal")}`⊤` gives a strictly greater result. -/
 lemma EReal.lt_add_of_pos_coe {x : EReal} {ε : ℝ} (hε : 0 < ε) (h_ne_bot : x ≠ ⊥) (h_ne_top : x ≠ ⊤) :
     x < x + ↑ε := by
   have h_eps : (0 : EReal) < (ε : EReal) := EReal.coe_pos.mpr hε
   have : 0 + x < ↑ε + x := EReal.add_lt_add_of_lt_of_le h_eps (le_refl x) h_ne_bot h_ne_top
   simpa [add_comm] using this
 
-/-- EReal epsilon argument: if for all positive ε, a ≤ b + ε, then a ≤ b.
+/-- {name}`EReal` epsilon argument: if for all positive ε, a ≤ b + ε, then a ≤ b.
     This holds when b ≠ ⊤ (if b = ⊤, the implication is trivially true). -/
 lemma EReal.le_of_forall_pos_le_add' {a b : EReal}
     (h : ∀ ε : ℝ, 0 < ε → a ≤ b + ε) : a ≤ b := by
@@ -108,7 +108,7 @@ lemma EReal.le_of_forall_pos_le_add' {a b : EReal}
         exact not_le.mpr (EReal.coe_lt_coe_iff.mpr h_ineq) h
 
 /-- Multiplication distributes over finite sums for EReal when all summands are non-negative.
-    This is needed because EReal lacks a general `LeftDistribClass` instance. -/
+    This is needed because EReal lacks a general {name}`LeftDistribClass` instance. -/
 lemma EReal.mul_finset_sum_of_nonneg (n : ℕ) (c : EReal) (f : Fin n → EReal) (hf : ∀ i, 0 ≤ f i) :
     c * (∑ i, f i) = ∑ i, c * f i := by
   induction n with
@@ -121,8 +121,8 @@ lemma EReal.mul_finset_sum_of_nonneg (n : ℕ) (c : EReal) (f : Fin n → EReal)
     congr 1
     exact ih (fun i => f i.castSucc) (fun i => hf _)
 
-/-- For non-negative reals, toEReal commutes with finite sums.
-    Uses induction on the finset with EReal.coe_add. -/
+/-- For non-negative reals, {name}`Real.toEReal` commutes with finite sums.
+    Uses induction on the finset with {name}`EReal.coe_add`. -/
 lemma EReal.coe_finset_sum {α : Type*} {s : Finset α} {f : α → ℝ}
     (hf : ∀ a ∈ s, 0 ≤ f a) :
     (∑ a ∈ s, f a).toEReal = ∑ a ∈ s, (f a).toEReal := by
@@ -162,10 +162,10 @@ lemma Summable.coe_ennreal {α : Type*} {f : α → ENNReal} :
   -- Summable follows from HasSum
   exact h_has_sum_coe.summable
 
-/-- Helper: Addition of tsums of ENNReal values coerced to EReal.
-    (∑' n, ↑(a n) : EReal) + (∑' n, ↑(b n) : EReal) = (∑' n, ↑(a n + b n) : EReal)
+/-- Helper: Addition of tsums of {name}`ENNReal` values coerced to {name}`EReal`.
+    {lean}`(∑' n, ↑(a n) : EReal) + (∑' n, ↑(b n) : EReal) = (∑' n, ↑(a n + b n) : EReal)`
 
-    This follows from ENNReal.tsum_add and the fact that coercion commutes with addition. -/
+    This follows from {name}`ENNReal.tsum_add` and the fact that coercion commutes with addition. -/
 lemma EReal.tsum_add_coe_ennreal {α : Type*} {a b : α → ENNReal} :
     (∑' n, ↑(a n) : EReal) + (∑' n, ↑(b n) : EReal) = (∑' n, ↑(a n + b n) : EReal) := by
   -- Use ENNReal.tsum_add: ∑' n, (a n + b n) = ∑' n, a n + ∑' n, b n
@@ -363,7 +363,7 @@ lemma EReal.coe_tsum_of_nonneg {g : ℕ → ℝ} (hg_nn : ∀ n, 0 ≤ g n) (hg_
   rw [h_lhs, h_rhs]
 
 /-- If all partial sums of a nonnegative EReal sequence are bounded by M, then the tsum is bounded by M.
-    This is a generalization of `ENNReal.tsum_le_of_sum_range_le` to EReal. -/
+    This is a generalization of {name}`ENNReal.tsum_le_of_sum_range_le` to EReal. -/
 lemma EReal.tsum_le_of_sum_range_le_of_nonneg {f : ℕ → EReal} {M : EReal}
     (h_nn : ∀ n, 0 ≤ f n) (h : ∀ N : ℕ, ∑ n ∈ Finset.range N, f n ≤ M) :
     ∑' n, f n ≤ M := by
@@ -424,7 +424,7 @@ lemma EReal.tsum_coe_ennreal_eq_top_of_tsum_eq_top {α : Type*} {f : α → ENNR
   simp only [h] at h_map
   exact h_map.symm
 
-/-- Tsum of a positive constant over an infinite type is ⊤ in EReal -/
+/-- Tsum of a positive constant over an infinite type is {lean (type := "EReal")}`⊤` in {name}`EReal` -/
 lemma EReal.tsum_const_eq_top_of_pos {α : Type*} [Infinite α] {c : EReal} (hc : 0 < c) :
     ∑' (_ : α), c = ⊤ := by
   by_cases h_top : c = ⊤
diff --git a/analysis/Analysis/Misc/SI.lean b/Analysis/Misc/SI.lean
similarity index 93%
rename from analysis/Analysis/Misc/SI.lean
rename to Analysis/Misc/SI.lean
index 3e11b102..2157df8b 100644
--- a/analysis/Analysis/Misc/SI.lean
+++ b/Analysis/Misc/SI.lean
@@ -3,7 +3,7 @@ import Analysis.Misc.UnitsSystem
 import Mathlib.Algebra.Group.MinimalAxioms
 
 
-/-- The SI unit system.  In order to permit fractional dimensions, we allow dimensions to be rational; but then to maintain defeq of various explicit dimensions, we need to unseal the arithmetic operations on the rationals. -/
+/-- The SI unit system.  In order to permit fractional dimensions, we allow dimensions to be rational; but then to maintain definitional equality of various explicit dimensions, we need to unseal the arithmetic operations on the rationals. -/
 @[ext]
 structure SI_dimensions where
   units_length : ℚ
@@ -20,8 +20,10 @@ instance SI_dimensions.instZero : Zero SI_dimensions where
 
 theorem SI_dimensions.zero_eq : (0:SI_dimensions) = ⟨ 0,0,0,0,0,0,0⟩ := rfl
 
-/-- The addition structure here is simple enough that one gets a lot of definitional equalities, e.g., between `d₁+d₂` and `d₂+d₁` for explicit choices of `d₁` and `d₂`,
-which is convenient as it means we do not need to utilize the `cast` operator much. -/
+/-- {given -show (type := "SI_dimensions")}`d₁, d₂`The addition structure here is simple enough that
+  one gets a lot of definitional equalities, e.g., between {lean}`d₁+d₂` and {lean}`d₂+d₁` for
+  explicit choices of {name}`d₁` and {name}`d₂`, which is convenient as it means we do not need to
+  utilize the {name (full := UnitsSystem.Scalar.cast)}`Scalar.cast` operator much. -/
 instance SI_dimensions.instAdd : Add SI_dimensions where
   add d₁ d₂ := ⟨d₁.units_length + d₂.units_length,
                 d₁.units_mass + d₂.units_mass,
@@ -74,7 +76,7 @@ abbrev SI : UnitsSystem := {
   addCommGroup := SI_dimensions.instAddCommGroup
 }
 
-/-- The SI system will be automatically installed as a global instance by any Lean file that imports this one.  This makes it difficult to use any competing unit system
+/-- The SI system will be automatically installed as a global instance by any Lean file that imports this one.  This makes it difficult to use any competing {name}`UnitsSystem`
 simultaneously, but that should be a rare use case. -/
 instance instSI : UnitsSystem := SI
 instance instSI_module : Module ℚ SI.Dimensions := SI_dimensions.instModule
diff --git a/analysis/Analysis/Misc/SIExamples.lean b/Analysis/Misc/SIExamples.lean
similarity index 100%
rename from analysis/Analysis/Misc/SIExamples.lean
rename to Analysis/Misc/SIExamples.lean
diff --git a/analysis/Analysis/Misc/UnitsSystem.lean b/Analysis/Misc/UnitsSystem.lean
similarity index 81%
rename from analysis/Analysis/Misc/UnitsSystem.lean
rename to Analysis/Misc/UnitsSystem.lean
index 2c894bc4..29aec340 100644
--- a/analysis/Analysis/Misc/UnitsSystem.lean
+++ b/Analysis/Misc/UnitsSystem.lean
@@ -3,6 +3,7 @@ import Mathlib.Algebra.Group.InjSurj
 import Mathlib.Order.Defs.PartialOrder
 import Mathlib.Algebra.Order.Module.Defs
 
+set_option doc.verso.suggestions false
 
 /-! A framework to formalize units (such as length, time, mass, velocity, etc.) in Lean.
 -/
@@ -35,19 +36,19 @@ namespace UnitsSystem
 
 variable [UnitsSystem]
 
-/-- The two key types here are `Formal` and `Scalar d`.  `Scalar d` is the space of scalar
-quantities whose units are given by `d:Dimensions`.  Collectively, they generate a graded commutative
- ring `Formal`, which can be conveniently described using the existing Mathlib structure
- `AddMonoidAlgebra`.  Algebraic manipulations of scalar quantities will be most conveniently
- handled by casting these quantities into the commutative ring  `Formal`, where one can use
- standard Mathlib tactics such as `ring`.
+/-- The two key types here are {name}`Formal` and `Scalar d`.  `Scalar d` is the space of scalar
+quantities whose units are given by `d : Dimensions`.  Collectively, they generate a graded commutative
+ ring {name}`Formal`, which can be conveniently described using the existing Mathlib structure
+ {name}`AddMonoidAlgebra`.  Algebraic manipulations of scalar quantities will be most conveniently
+ handled by casting these quantities into the commutative ring {name}`Formal`, where one can use
+ standard Mathlib tactics such as {name (full := Mathlib.Tactic.RingNF.ring)}`ring`.
 
 In principle one could also develop vector-valued quantities with dimension, but for now we
 restrict attention to scalar quantities only.
 -/
 abbrev Formal := AddMonoidAlgebra ℝ Dimensions
 
-/-- The data `val` of a scalar quantity can be interpreted as the numerical value of that
+/-- The data {name}`Scalar.val` of a {name}`Scalar` quantity can be interpreted as the numerical value of that
 quantity with respect to some standard set of units (e.g., SI units). -/
 @[ext]
 structure Scalar (d:Dimensions) where
@@ -63,18 +64,18 @@ theorem Scalar.val_inj {d:Dimensions} (q₁ q₂:Scalar d) :
   q₁.val = q₂.val ↔ q₁ = q₂ := Scalar.val_injective _ |>.eq_iff
 
 
-/-- We will encounter a technical issue with Lean's type system, namely that the type `Scalar d`
-and `Scalar d'` are not identical if `d'` and `d` are merely propositionally equal (as opposed
-to definitionally equal); for instance, `Scalar (d₁+d₂)` and `Scalar (d₂+d₁)` are distinct types.
+/-- {given -show}`d, d', d₁, d₂` We will encounter a technical issue with Lean's type system, namely that the type {lean}`Scalar d`
+and {lean}`Scalar d'` are not identical if {name}`d'` and {name}`d` are merely propositionally equal (as opposed
+to definitionally equal); for instance, {lean}`Scalar (d₁+d₂)` and {lean}`Scalar (d₂+d₁)` are distinct types.
 Technically, this renders multiplication on scalar types noncommutative. To get around this, we
 create a casting operator, where the propositional equality is attempted to be resolved by the Lean
-tactic `module` whenever possible.  Unfortunately, the casting operator from `Scalar d` to `Scalar d'`
-cannot be captured by standard Lean coercion classes such as `Coe` or `CoeOut` as each of the types
-here contain parameters not present in the other.-/
+tactic {tactic}`module` whenever possible.  Unfortunately, the casting operator from {lean}`Scalar d` to {lean}`Scalar d'`
+cannot be captured by standard Lean coercion classes such as {name}`Coe` or {name}`CoeOut` as each of the types
+here contain parameters not present in the other. -/
 def Scalar.cast {d d':Dimensions}  (q: Scalar d) (_ : d' = d := by module) : Scalar d' :=
   ⟨q.val⟩
 
-/-- This is a variant of `Scalar.val_inj` that handles casts.-/
+/-- This is a variant of {name}`Scalar.val_inj` that handles casts. -/
 theorem Scalar.cast_eq {d d':Dimensions} (q: Scalar d) (q': Scalar d') (h: d = d' := by module)
   : q.val = q'.val ↔ q = q'.cast h := by aesop
 
@@ -85,8 +86,8 @@ theorem Scalar.cast_eq_symm {d d':Dimensions} (q: Scalar d) (q': Scalar d') (h:
 theorem Scalar.cast_val {d d':Dimensions} (q: Scalar d) (h: d' = d := by module)
   : (q.cast h).val = q.val := by aesop
 
-/-- The existing Mathlib method `AddMonoidAlgebra.single` is perfect for embedding each type of
-scalar into the formal graded ring `Formal`. -/
+/-- The existing Mathlib method {name}`AddMonoidAlgebra.single` is perfect for embedding each type of
+{name}`Scalar` into the formal graded ring {name}`Formal`. -/
 @[coe]
 noncomputable def Scalar.toFormal {d:Dimensions} (q:Scalar d) : Formal :=
   AddMonoidAlgebra.single d q.val
@@ -94,11 +95,11 @@ noncomputable def Scalar.toFormal {d:Dimensions} (q:Scalar d) : Formal :=
 noncomputable instance Scalar.instCoeFormal (d: Dimensions) : CoeOut (Scalar d) Formal where
   coe := toFormal
 
-/-- Many identities  involving several types of `Scalar`s can be dealt with by applying
-`simp [←toFormal_inj]` to move everything to `Formal`.  A large number of further `simp` lemmas
-in this file are then designed to simplify such `Formal` expressions, often by pushing casting
-operators inward back to the `Scalar` types.  As such, there will be significant overlap between
-the `simp` and `norm_cast` tags. -/
+/-- Many identities involving several types of {name}`Scalar`s can be dealt with by applying
+{syntax tactic}`simp [←toFormal_inj]` to move everything to {name}`Formal`.  A large number of further {tactic}`simp` lemmas
+in this file are then designed to simplify such {name}`Formal` expressions, often by pushing casting
+operators inward back to the {name}`Scalar` types.  As such, there will be significant overlap between
+the {tactic}`simp` and {tactic}`norm_cast` tags. -/
 @[simp]
 theorem Scalar.toFormal_inj {d: Dimensions} (q₁ q₂:Scalar d) :
   (q₁:Formal) = (q₂:Formal) ↔ q₁ = q₂ := by
@@ -109,7 +110,7 @@ theorem Scalar.toFormal_inj {d: Dimensions} (q₁ q₂:Scalar d) :
   intro h; simp [h]
 
 /-- Conveniently, casts from one scalar to another will automatically disappear when moving to
-`Formal`. -/
+{name}`Formal`. -/
 @[simp]
 theorem Scalar.toFormal_cast {d d': Dimensions} (q:Scalar d) (h:d' = d := by module) :
   ((q.cast h):Formal) = (q:Formal) := by
@@ -122,8 +123,8 @@ instance Scalar.instZero {d:Dimensions} : Zero (Scalar d) where
 @[simp]
 theorem Scalar.val_zero {d:Dimensions} : (0:Scalar d).val = 0 := rfl
 
-/-- We will use the `NeZero` class to tag some scalars as non-zero; this becomes relevant when
-using such scalars as units.   One could also introduce API to tag some scalars as positive, but
+/-- We will use the {name}`NeZero` class to tag some scalars as non-zero; this becomes relevant when
+using such scalars as units.  One could also introduce API to tag some scalars as positive, but
 we currently are not implementing this. -/
 theorem Scalar.neZero_iff {d:Dimensions} (q:Scalar d) : NeZero q ↔ q.val ≠ 0 := by simp [_root_.neZero_iff, ←val_inj]
 
@@ -132,15 +133,15 @@ theorem Scalar.toFormal_zero {d:Dimensions} : ((0:Scalar d):Formal) = 0 := by
   simp only [toFormal, AddMonoidAlgebra.single, val_zero, Finsupp.single_zero]
   rfl
 
-/-- In the next few lines of code we give `Scalar d` the structure of a real vector space,
-which is of course compatible with the real vector space structure on `Formal`. -/
+/-- In the next few lines of code we give {lean}`Scalar d` the structure of a real vector space,
+which is of course compatible with the real vector space structure on {name}`Formal`.  -/
 instance Scalar.instAdd {d:Dimensions} : Add (Scalar d) where
   add q₁ q₂ := ⟨q₁.val + q₂.val⟩
 
 @[simp]
 theorem Scalar.val_add {d:Dimensions} (q₁ q₂:Scalar d) : (q₁ + q₂).val = q₁.val + q₂.val := rfl
 
-/-- Note how the `simp` lemma is in the direction of pushing casts inward. -/
+/-- Note how the {tactic}`simp` lemma is in the direction of pushing coercions inward. -/
 @[simp,norm_cast]
 theorem Scalar.toFormal_add {d:Dimensions} (q₁ q₂:Scalar d) : ((q₁ + q₂:Scalar d):Formal) = (q₁:Formal) + (q₂:Formal) := by
   simp only [toFormal, val_add, Finsupp.single_add]
@@ -182,7 +183,7 @@ instance Scalar.instAddGroup {d:Dimensions} : AddGroup (Scalar d) :=
 instance Scalar.instAddCommGroup {d:Dimensions} : AddCommGroup (Scalar d) :=
   val_injective _ |>.addCommGroup _ val_zero val_add val_neg val_sub (Function.swap val_smul) (Function.swap val_smul)
 
-/-- The dimensionless scalars `Scalar 0` can be identified with real numbers. -/
+/-- The dimensionless scalars {lean}`Scalar 0` can be identified with real numbers.  -/
 @[coe]
 def Scalar.ofReal (r:ℝ) : Scalar 0 := ⟨ r ⟩
 
@@ -212,8 +213,8 @@ theorem Scalar.coe_neg (r:ℝ) : ((-r:ℝ):Scalar 0) = -(r:Scalar 0) := rfl
 theorem Scalar.coe_sub (r s:ℝ) : ((r-s:ℝ):Scalar 0) = (r:Scalar 0) - (s:Scalar 0) := by
   simp [ofReal]; rfl
 
-/-- It is convenient to view the real numbers as a subring of the `Formal` ring, thus identifying
-scalar multiplication with ordinary multiplication. -/
+/-- It is convenient to view the real numbers as a subring of the {name}`Formal` ring, thus identifying
+{name}`Scalar` multiplication with ordinary multiplication. -/
 noncomputable instance Formal.instCoeReal : Coe ℝ Formal where
   coe r := ((r:Scalar 0):Formal)
 
@@ -256,7 +257,7 @@ theorem Formal.smul_eq_mul'' (c:ℤ) (x:Formal) : c • x = (c:Formal) * x := by
 theorem Scalar.coe_mul (r s:ℝ) : ((r*s:ℝ):Scalar 0) = r • (s:Scalar 0) := by
   ext; simp [ofReal]
 
-/-- We are finally able to view `Scalar` as a vector space over `ℝ` as promised. -/
+/-- We are finally able to view {lean}`Scalar d` as a vector space over {lean}`ℝ` as promised. -/
 instance Scalar.instModule {d:Dimensions} : Module ℝ (Scalar d) where
   smul_add c q₁ q₂ := by simp [←toFormal_inj]; ring
   add_smul c1 c2 q := by simp [←toFormal_inj]; ring
@@ -281,8 +282,8 @@ theorem Scalar.toFormal_smul'' {d:Dimensions} (c:ℤ) (q:Scalar d)
   : ((c • q:Scalar d):Formal) = (c:Formal) * (q:Formal) := by
   simp [←Int.cast_smul_eq_zsmul ℝ]
 
-/-- One can multiply a `Scalar d₁` and `Scalar d₂` quantities to obtain a `Scalar (d₁+d₂)` quantity,
-in a manner compatible with multiplication in `Formal`. -/
+/-- One can multiply a {lean}`Scalar d₁` and {lean}`Scalar d₂` quantities to obtain a {lean}`Scalar (d₁+d₂)` quantity,
+in a manner compatible with multiplication in {name}`Formal`. -/
 instance Scalar.instHMul {d₁ d₂:Dimensions} : HMul (Scalar d₁) (Scalar d₂) (Scalar (d₁ + d₂)) where
   hMul q₁ q₂ := ⟨q₁.val * q₂.val⟩
 
@@ -295,11 +296,11 @@ theorem Scalar.toFormal_hMul {d₁ d₂:Dimensions} (q₁:Scalar d₁) (q₂:Sca
   ((q₁ * q₂:Scalar _):Formal) = (q₁:Formal) * (q₂:Formal) := by
   simp [toFormal, AddMonoidAlgebra.single_mul_single]
 
-/-- Similarly, one can raise a `Scalar d` quantity to a natural number power `n` to obtain a `Scalar (n • d)` quantity.  One could also implement exponentiation to an integer, but I have elected
+/-- Similarly, one can raise a {lean}`Scalar d` quantity to a natural number power {name}`n` to obtain a {lean}`Scalar (n • d)` quantity.  One could also implement exponentiation to an integer, but I have elected
 not to do this, implementing an inversion relation instead. -/
 noncomputable def Scalar.pow {d:Dimensions} (q: Scalar d) (n:ℕ) : Scalar (n • d) := ⟨ q.val^n ⟩
 
-/-- One cannot use the Mathlib classes `Pow` or `HPow` here because the output type `Scalar (n • d)` depends on the input `n`.  As the symbol `^` is reserved for such classes, we use the symbol `**` isntead.-/
+/-- {given -show}`n : ℕ, d` One cannot use the Mathlib classes {name}`Pow` or {name}`HPow` here because the output type {lean}`Scalar (n • d)` depends on the input {name}`n`.  As the symbol {kw (of := «term_^_»)}`^` is reserved for such classes, we use the symbol `**` instead.-/
 infix:80 "**" => Scalar.pow
 
 @[simp]
@@ -311,7 +312,7 @@ theorem Scalar.toFormal_pow {d:Dimensions} (q:Scalar d) (n:ℕ) :
   ((q ** n):Formal) = (q:Formal) ^ n := by
   simp [toFormal, AddMonoidAlgebra.single_pow]
 
-/-- We cannot use Mathlib's `Inv` class here or the associated `⁻¹` notation because `Inv` requires the output to be of the same type as the input. -/
+/-- We cannot use Mathlib's {name}`Inv` class here or the associated {kw (of := «term_⁻¹»)}`⁻¹` notation because {name}`Inv` requires the output to be of the same type as the input. -/
 noncomputable def Scalar.inv {d:Dimensions} (q:Scalar d) : Scalar (-d) := ⟨ q.val⁻¹ ⟩
 
 @[simp]
@@ -425,7 +426,7 @@ noncomputable instance Scalar.instIsStrictOrderedModule (d:Dimensions) : IsStric
 
 -- TODO: add in some `gcongr` lemmas for this order
 
-/-- The standard unit of `Scalar d` is the quantity whose data `val` is equal to 1. -/
+/-- The standard unit of {lean}`Scalar d` is the quantity whose data {name}`Scalar.val` is equal to {lean (type := "ℝ")}`1`. -/
 def StandardUnit (d:Dimensions) : Scalar d := ⟨ 1 ⟩
 
 @[simp]
@@ -458,7 +459,7 @@ theorem StandardUnit.inv (d:Dimensions) : (StandardUnit d).inv = StandardUnit (-
 theorem StandardUnit.div (d₁ d₂:Dimensions) : StandardUnit d₁ / StandardUnit d₂ = StandardUnit (d₁-d₂) := by
   simp [←Scalar.val_inj]
 
-/-- `unit.in q` is `q:Scalar d` measured in terms of `unit:Scalar d`. -/
+/-- {lean}`unit.in q` is {lean}`q : Scalar d` measured in terms of {lean}`unit : Scalar d`. -/
 noncomputable def Scalar.in {d:Dimensions} (unit q:Scalar d) : ℝ := q.val / unit.val
 
 @[simp]
diff --git a/analysis/Analysis/Misc/UnitsSystemExamples.lean b/Analysis/Misc/UnitsSystemExamples.lean
similarity index 58%
rename from analysis/Analysis/Misc/UnitsSystemExamples.lean
rename to Analysis/Misc/UnitsSystemExamples.lean
index 31933688..5b0f41fa 100644
--- a/analysis/Analysis/Misc/UnitsSystemExamples.lean
+++ b/Analysis/Misc/UnitsSystemExamples.lean
@@ -4,12 +4,13 @@ import Analysis.Misc.UnitsSystem
 open UnitsSystem
 variable [UnitsSystem]
 
-/- Many algebraic identities involving `Scalar` can be established by first using `simp [←toFormal_inj]`  to coerce to `Formal` and  push coercions inside, then appealing to `ring`.  We give some examples below.
+/-! Many algebraic identities involving {name}`Scalar` can be established by first using {syntax tactic}`simp [←toFormal_inj]`  to coerce to {name}`Formal` and  push coercions inside, then appealing to {tactic}`ring`.  We give some examples below.
 
-Alternatively, one can "work in coordinates" by using `simp [←val_inj]` in place of `simp [←toFormal_inj]`.
+Alternatively, one can "work in coordinates" by using {syntax tactic}`simp [←val_inj]` in place of {syntax tactic}`simp [←toFormal_inj]`.
 -/
 
-/-- A cast is needed here because `(d₁+d₂)+d₃` is not definitionally equal to `d₁+(d₂+d₃)`. -/
+/-- {given -show (type := "Dimensions")}`d₁, d₂, d₃` A {name}`Scalar.cast` is needed here because
+  {lean}`(d₁+d₂)+d₃` is not definitionally equal to {lean}`d₁+(d₂+d₃)`. -/
 theorem UnitsSystem.Scalar.hMul_assoc {d₁ d₂ d₃:Dimensions} (a:Scalar d₁) (b:Scalar d₂) (c:Scalar d₃):
   a * (b * c) = ((a * b) * c).cast := by
   simp [←toFormal_inj]; ring
@@ -22,7 +23,7 @@ theorem UnitsSystem.Scalar.right_distrib {d₁ d₂:Dimensions} (a b:Scalar d₁
   (a + b) * c = (a * c) + (b * c) := by
   simp [←toFormal_inj]; ring
 
-/-- A cast is needed here because `2 • d` is not definitionally equal to `d+d`. -/
+/-- A {name}`Scalar.cast` is needed here because {lean}`2 • d` is not definitionally equal to {lean}`d+d`. -/
 theorem UnitsSystem.Scalar.sq_add {d:Dimensions} (a b:Scalar d) : (a+b)**2 = a**2 + (2 • a * b).cast + b**2 := by
   simp [←toFormal_inj]; ring
 
diff --git a/analysis/Analysis/Misc/equational.lean b/Analysis/Misc/equational.lean
similarity index 100%
rename from analysis/Analysis/Misc/equational.lean
rename to Analysis/Misc/equational.lean
diff --git a/analysis/Analysis/Misc/erdos_379.lean b/Analysis/Misc/erdos_379.lean
similarity index 86%
rename from analysis/Analysis/Misc/erdos_379.lean
rename to Analysis/Misc/erdos_379.lean
index a514ea57..764c2ecb 100644
--- a/analysis/Analysis/Misc/erdos_379.lean
+++ b/Analysis/Misc/erdos_379.lean
@@ -4,7 +4,7 @@ import Mathlib
 
 open Nat
 
-/-- $$\binom{n}{k} \cdot k = \binom{n-1}{k-1} \cdot n$$. -/
+/-- $$`\binom\{n\}\{k\} \cdot k = \binom\{n-1\}\{k-1\} \cdot n`. -/
 theorem binom_eq {n k:ℕ} (hk: 1 ≤ k) : (n.choose k) * k = ((n-1).choose (k-1)) * n := by
   rcases le_or_gt k n with _ | hn
   . symm; rw [←choose_symm]; nth_rewrite 2 [←choose_symm]
@@ -12,7 +12,7 @@ theorem binom_eq {n k:ℕ} (hk: 1 ≤ k) : (n.choose k) * k = ((n-1).choose (k-1
     all_goals omega
   simp [choose_eq_zero_of_lt hn, choose_eq_zero_iff]; omega
 
-/-- $$\binom{n}{k} \cdot k \cdot (k-1) = \binom{n-2}{k-2} \cdot (n-1) \cdot n$$.-/
+/-- $$`\binom\{n\}\{k\} \cdot k \cdot (k-1) = \binom\{n-2\}\{k-2\} \cdot (n-1) \cdot n`.-/
 theorem binom_eq_2 {n k:ℕ} (hk: 2 ≤ k) : (n.choose k) * k * (k-1) = ((n-2).choose (k-2)) * (n-1) * n := calc
   _ = ((n-1).choose (k-1)) * n * (k-1) := by rw [binom_eq]; omega
   _ = ((n-1).choose (k-1)) * (k-1) * n := by ring
@@ -20,13 +20,13 @@ theorem binom_eq_2 {n k:ℕ} (hk: 2 ≤ k) : (n.choose k) * k * (k-1) = ((n-2).c
     rw [binom_eq]; congr 2
     all_goals omega
 
-/-- If $$p^{a+b+1} \mid n$$, then $$p^{a+1} \mid \binom{n}{k}$$ or $$p^{b+1} \mid k$$. -/
+/-- If $$`p^\{a+b+1\} \mid n$$, then $$p^\{a+1\} \mid \binom\{n\}\{k\}$$ or $$p^\{b+1\} \mid k`. -/
 theorem lemma_1 {n k p a b:ℕ} (hk: 1 ≤ k)
  (hp: p.Prime) (h1: p^(a+b+1) ∣ n) : p^(a+1) ∣ n.choose k ∨ p^(b+1) ∣ k := by
   replace h1 := h1.trans (dvd_mul_left _ ((n-1).choose (k-1)))
   rw [←binom_eq hk] at h1; contrapose! h1; apply finiteMultiplicity_mul_aux hp.prime <;> tauto
 
-/-- If $$p^r \mid n-1$$ and $$k,n-k$$ are not divisible by $$p$$, then $$p^r \mid \binom{n}{k}$$. -/
+/-- If $$`p^r \mid n-1$$ and $$k,n-k$$ are not divisible by $$p$$, then $$p^r \mid \binom\{n\}\{k\}`. -/
 theorem lemma_2 {n k p r:ℕ} (hk: 2 ≤ k) (hn: k ≤ n)
  (hp: p.Prime) (h1: p^r ∣ n-1) (hr: 0 < r) (h2: ¬p∣k) (h3: ¬ p∣n-k) : p^r ∣ n.choose k := by
   have h1' : p ∣ n-1 := (dvd_pow_self _ (by omega)).trans h1
@@ -35,7 +35,7 @@ theorem lemma_2 {n k p r:ℕ} (hk: 2 ≤ k) (hn: k ≤ n)
   replace h3 : ¬p∣k-1 := by contrapose! h3; convert dvd_sub h1' h3 using 1; omega
   exact hp.prime.pow_dvd_of_dvd_mul_right _ h2 (hp.prime.pow_dvd_of_dvd_mul_right _ h3 h1)
 
-/-- If $$n=2^{\phi(p^R)}$$ and $$p>2^{r-1}$$, then $$2^r \mid \binom{n}{k}$$ or $$p^R \mid \binom{n}{k}$$.-/
+/-- If $$`n=2^\{\phi(p^R)\}$$ and $$p>2^\{r-1\}$$, then $$2^r \mid \binom\{n\}\{k\}$$ or $$p^R \mid \binom\{n\}\{k\}`.-/
 theorem key_prop {k n p r R:ℕ} (hn: n = 2^((p^R).totient))
   (hk: 1 ≤ k) (hkn: k < n) (hp: p.Prime) (hpr: p > 2^(r-1))
   (hr: 1 < r) (hr' : r ≤ (p^R).totient):
@@ -62,7 +62,7 @@ theorem key_prop {k n p r R:ℕ} (hn: n = 2^((p^R).totient))
 
 noncomputable abbrev S (n:ℕ) : ℕ := sSup { r | ∀ k ∈ Finset.Ico 1 n, ∃ p, p.Prime ∧ p^r ∣ (n.choose k) }
 
-/-- The condition `1<n` is necessary to avoid the range of `k` being vacuous. -/
+/-- The condition {lean}`1<n` is necessary to avoid the range of {lit}`k` being vacuous. -/
 theorem S_ge {n r:ℕ} (hn: 1 < n) (h: ∀ k ∈ Finset.Ico 1 n, ∃ p, p.Prime ∧ p^r ∣ n.choose k) : r ≤ S n := by
   apply le_csSup
   . rw [bddAbove_def]; use n; simp; intro r h
@@ -71,7 +71,7 @@ theorem S_ge {n r:ℕ} (hn: 1 < n) (h: ∀ k ∈ Finset.Ico 1 n, ∃ p, p.Prime
     all_goals grind
   aesop
 
-/-- If $$p>2^{r-1}$$, then $$S(2^{\phi(p^R)}) \ge r$$.-/
+/-- If $$p>2^\{r-1\}$$, then $$S(2^\{\phi(p^R)\}) \ge r$$.-/
 theorem key_cor {p r:ℕ} (hp: p.Prime) (hpr: p > 2^(r-1)) (hr: 1 < r) :
   r ≤ S (2^((p^r).totient)) := by
   apply S_ge; simp; grind
@@ -92,11 +92,10 @@ theorem erdos_379 : Filter.atTop.limsup (fun n ↦ (S n:ENat)) = ⊤ := by
   simp; intro N; rw [iSup₂_eq_top]; intro r hr; lift r to ℕ using (by order)
   have ⟨ p, hp, hp' ⟩ := exists_infinite_primes (max N (2^(r+1)+1))
   use 2^((p^(r+2)).totient), ?_
-  . have := key_cor hp' (r := r+2) ?_ ?_ <;> simp at *
-    all_goals first | linarith | (rw [ENat.coe_lt_coe]; omega)
+  . have := key_cor hp' (r := r+2) ?_ ?_ <;> simp at * <;> grind
   trans p; order
   have := hp'.one_lt
   have := (p-1).lt_two_pow_self
   have : 2^(p-1) ≤ 2 ^ (p ^ (r + 2)).totient := by
     rw [totient_prime_pow hp']; gcongr; simp; apply Nat.le_mul_of_pos_left; positivity; omega
-  omega
+  grind
diff --git a/analysis/Analysis/Misc/erdos_613.lean b/Analysis/Misc/erdos_613.lean
similarity index 88%
rename from analysis/Analysis/Misc/erdos_613.lean
rename to Analysis/Misc/erdos_613.lean
index c9790bd3..9a0d7789 100644
--- a/analysis/Analysis/Misc/erdos_613.lean
+++ b/Analysis/Misc/erdos_613.lean
@@ -6,9 +6,10 @@ open scoped BigOperators
 
 -- 1. Define the main claim
 
-/-- “Color-`col` monochromatic star of size `k`”: there is a center `x` and a set `S`
-    of `k` distinct neighbors of `x` such that every edge `{x,y}` with `y ∈ S`
-    is present in `G` and colored `col`.  (No restriction on edges inside `S`.) -/
+/-- “Color-{name}`col` monochromatic star of size {name}`k`”: there is a center {given}`x` and a set
+    {given (type := "Finset V")}`S` of {name}`k` distinct neighbors of {name}`x` such that every
+    edge {given -show}`y` {lean}`s(x, y)` with {lean}`y ∈ S` is present in {lean}`G` and colored
+    {name}`col`.  (No restriction on edges inside {name}`S`.) -/
 def hasMonoStar {V:Type*} (G : SimpleGraph V) (color : Sym2 V → Fin 2)
     (col : Fin 2) (k : ℕ) : Prop :=
   ∃ (x : V) (S : Finset V),
@@ -16,8 +17,11 @@ def hasMonoStar {V:Type*} (G : SimpleGraph V) (color : Sym2 V → Fin 2)
     x ∉ S ∧
     ∀ ⦃y : V⦄, y ∈ S → G.Adj x y ∧ color (s(x, y)) = col
 
-/-- “Color-`col` monochromatic triangle”: there exist `a b c` with all three edges
-    present in `G` and colored `col`.  (Adjacency already forces distinctness.) -/
+/--
+{given -show}`a, b, c : V`
+“Color-{name}`col` monochromatic triangle”: there exist {name}`a`, {name}`b`, {name}`c` with all three edges
+present in {lean}`G` and colored {name}`col`.  (Adjacency already forces distinctness.)
+-/
 def hasMonoTriangle {V:Type*} (G : SimpleGraph V) (color : Sym2 V → Fin 2)
     (col : Fin 2) : Prop :=
   ∃ a b c : V,
@@ -27,11 +31,11 @@ def hasMonoTriangle {V:Type*} (G : SimpleGraph V) (color : Sym2 V → Fin 2)
     color (s(a, c)) = col
 
 /-- **Statement (n = 5 case of Pikhurko’s counterexample).**
-There exists a simple graph on `16` vertices with exactly `44` edges such that
-for *every* 2‑coloring of unordered pairs, either color `0` contains a `K_{1,5}`
-(a 5‑edge star) or color `1` contains a `K₃` (a triangle).
+There exists a simple graph on {lean}`16` vertices with exactly {lean}`44` edges such that
+for *every* 2‑coloring of unordered pairs, either color {lean (type := "Fin 2")}`0` contains a $`K_{1,5}`
+(a 5‑edge star) or color {lean (type := "Fin 2")}`1` contains a $`K₃` (a triangle).
 
-This only *states* the claim (as a `Prop`).  You can later prove it from the
+This only *states* the claim (as a {lean}`Prop`).  You can later prove it from the
 explicit construction, or assume it as an axiom while you develop the rest. -/
 def Pikhurko_n5_statement : Prop :=
   ∃ (V:Type) (G : SimpleGraph V),
@@ -57,11 +61,11 @@ open V
 
 /-- Adjacency relation for the Pikhurko n=5 counterexample.
 
-* Inside `A1` and inside `A2`: cliques.
-* Between `A1`–`B1` and `A2`–`B2`: complete bipartite.
-* Inside `B1` and `B2`: no edges.
-* No edges between the two blocks `{A1,B1}` and `{A2,B2}`.
-* `apex` is connected to every non-`apex` vertex. -/
+* Inside {name}`A1` and inside {name}`A2`: cliques.
+* Between {name}`A1`–{name}`B1` and {name}`A2`–{name}`B2`: complete bipartite.
+* Inside {name}`B1` and {name}`B2`: no edges.
+* No edges between the two blocks {name}`A1`/{name}`B1` and {name}`A2`/{name}`B2`.
+* {name}`apex` is connected to every non-{name}`apex` vertex. -/
 def GAdj : V → V → Prop
 | apex, apex => False
 | apex, _    => True
@@ -74,7 +78,7 @@ def GAdj : V → V → Prop
 | B2 _, A2 _ => True
 | _,    _    => False
 
-/-- The graph `G` on 16 vertices used for the n=5 counterexample. -/
+/-- The graph {name}`G` on 16 vertices used for the n=5 counterexample. -/
 def G : SimpleGraph V where
   Adj := GAdj
   symm := by
@@ -143,7 +147,7 @@ open V
 /- We’ll need `Fintype` on `V` for `univ`, sums, etc. -/
 deriving instance Fintype for V
 
-/-- An explicit equivalence showing `V` has 2+5+3+5+1 = 16 elements. -/
+/-- An explicit equivalence showing {name}`V` has 2+5+3+5+1 = 16 elements. -/
 def VEquiv :
     V ≃ ((((Fin 2 ⊕ Fin 5) ⊕ Fin 3) ⊕ Fin 5) ⊕ Unit) where
   toFun
@@ -161,7 +165,7 @@ def VEquiv :
   left_inv v := by cases v <;> grind
   right_inv w := by cases w <;> grind
 
-/-- `|V| = 16`. Useful for quick cardinality arithmetic. -/
+/-- $`|V| = 16`. Useful for quick cardinality arithmetic. -/
 lemma card_V : Fintype.card V = 16 := by
   -- Reduce to the nested-sum cardinality and compute arithmetically.
   simpa using
@@ -170,11 +174,11 @@ lemma card_V : Fintype.card V = 16 := by
         -- `simp` turns cardinals of sums into sums of cardinals; `norm_num` does the rest.
         simp [Fintype.card_sum, Fintype.card_fin]
 
-/-! ## Degree computations
+/-! # Degree computations
 
-We compute the degree of each vertex *kind*. We’ll use your `[simp]` adjacency
+We compute the degree of each vertex *kind*. We’ll use your {attr}`@[simp]` adjacency
 lemmas from Approach A:
-- `adj_apex_left`, `adj_A1A1`, `adj_A2A2`, `adj_A1B1`, `adj_A2B2`,
+- {name}`adj_apex_left`, {name}`adj_A1A1`, {name}`adj_A2A2`, {name}`adj_A1B1`, {name}`adj_A2B2`,
   and the corresponding “no edge” lemmas across blocks.
 -/
 
@@ -204,7 +208,7 @@ lemma degree_apex : G.degree apex = 15 := by
   simp at this
   assumption
 
-/-- `deg(A1 i) = 7` for each `i`. -/
+/-- `deg(A1 i) = 7` for each {name}`i`. -/
 lemma degree_A1 (i : Fin 2) : G.degree (A1 i) = 7 := by
   rw [←G.card_neighborFinset_eq_degree, ←Finset.card_image_of_injective _ VEquiv.injective]
   simp_rw [←Finset.card_toLeft_add_card_toRight]
@@ -248,7 +252,7 @@ lemma degree_A1 (i : Fin 2) : G.degree (A1 i) = 7 := by
         _ = 1 := by simp
     _ = _ := by norm_num
 
-/-- `deg(B1 j) = 3` for each `j`. (Two `A1`s + apex.) -/
+/-- $`deg(B1 j) = 3` for each $`j`. (Two {name}`A1`s + apex.) -/
 lemma degree_B1 (j : Fin 5) : G.degree (B1 j) = 3 := by
   rw [←G.card_neighborFinset_eq_degree, ←Finset.card_image_of_injective _ VEquiv.injective]
   simp_rw [←Finset.card_toLeft_add_card_toRight]
@@ -289,7 +293,7 @@ lemma degree_B1 (j : Fin 5) : G.degree (B1 j) = 3 := by
 
 
 
-/-- `deg(A2 i) = 8` for each `i`. (Two inside `A2` + five in `B2` + apex.) -/
+/-- $`deg(A2 i) = 8` for each $`i`. (Two inside {name}`A2` + five in {name}`B2` + apex.) -/
 lemma degree_A2 (i : Fin 3) : G.degree (A2 i) = 8 := by
   rw [←G.card_neighborFinset_eq_degree, ←Finset.card_image_of_injective _ VEquiv.injective]
   simp_rw [←Finset.card_toLeft_add_card_toRight]
@@ -332,7 +336,7 @@ lemma degree_A2 (i : Fin 3) : G.degree (A2 i) = 8 := by
     _ = _ := by norm_num
 
 
-/-- `deg(B2 j) = 4` for each `j`. (Three `A2`s + apex.) -/
+/-- $`deg(B2 j) = 4` for each $`j`. (Three {name}`A2`s + apex.) -/
 lemma degree_B2 (j : Fin 5) : G.degree (B2 j) = 4 := by
   rw [←G.card_neighborFinset_eq_degree, ←Finset.card_image_of_injective _ VEquiv.injective]
   simp_rw [←Finset.card_toLeft_add_card_toRight]
@@ -372,7 +376,7 @@ lemma degree_B2 (j : Fin 5) : G.degree (B2 j) = 4 := by
     _ = _ := by norm_num
 
 /-!
-### Edge count via the handshaking lemma
+# Edge count via the handshaking lemma
 We now sum the degrees and divide by 2.
 -/
 theorem edge_count_44 : G.edgeSet.ncard = 44 := by
@@ -399,7 +403,7 @@ end PikhurkoN5
 namespace PikhurkoN5
 open V
 
-/-! ### Small utilities -/
+/-! # Small utilities -/
 
 /- Pick a `k`-subset of a finset `s` when `k ≤ s.card`. -/
 namespace Finset
@@ -411,17 +415,17 @@ lemma exists_subset_card_eq (s : Finset α) {k : ℕ} (hk : k ≤ s.card) :
 
 end Finset
 
-/-- In `Fin 2`, saying “equals `1`” is the same as “not equal to `0`”. -/
+/-- In {lean}`Fin 2`, saying “equals {lean (type := "Fin 2")}`1`” is the same as “not equal to {lean (type := "Fin 2")}`0`”. -/
 lemma fin2_eq_one_iff_ne_zero (a : Fin 2) : (a = 1) ↔ a ≠ 0 := by
   fin_cases a <;> simp
 
-/-! ### Red neighbors of the apex are ≥ 11 if there is no blue star K_{1,5} -/
+/-! # Red neighbors of the apex are ≥ 11 if there is no blue star `K_{1,5}` -/
 
-/-- The set of blue neighbors of `apex` in color class `0`. -/
+/-- The set of blue neighbors of {name}`apex` in color class {lean (type := "Fin 2")}`0`. -/
 noncomputable def blueNeighbors (color : Sym2 V → Fin 2) : Finset V :=
   (G.neighborFinset apex).filter (fun v => color (s(apex, v)) = 0)
 
-/-- The set of red neighbors of `apex` in color class `1`. -/
+/-- The set of red neighbors of {name}`apex` in color class {lean (type := "Fin 2")}`1`. -/
 noncomputable def redNeighbors (color : Sym2 V → Fin 2) : Finset V :=
   (G.neighborFinset apex).filter (fun v => color (s(apex, v)) = 1)
 
@@ -463,7 +467,7 @@ lemma blueNeighbors_card_le_4
 
   exact hNoBlueStar hstar
 
-/-- If there is no blue `K_{1,5}`, then at least `11` neighbors of `apex` are red. -/
+/-- If there is no blue `K_{1,5}`, then at least {lean}`11` neighbors of {name}`apex` are red. -/
 lemma red_from_apex_at_least_11
     (color : Sym2 V → Fin 2)
     (hNoBlueStar : ¬ hasMonoStar G color 0 5) :
@@ -526,7 +530,7 @@ end PikhurkoN5
 namespace PikhurkoN5
 open V
 
-/-- Membership in the first block `{A1, B1}`. -/
+/-- Membership in the first block {name}`A1`/{name}`B1`. -/
 def inBlock1 : V → Prop
 | A1 _ => True
 | B1 _ => True
@@ -535,18 +539,18 @@ def inBlock1 : V → Prop
 noncomputable instance : DecidablePred inBlock1 := by
   intro v; cases v <;> infer_instance
 
-/-- Red neighbors of `apex` that lie in the first block `{A1,B1}`. -/
+/-- Red neighbors of {name}`apex` that lie in the first block {name}`A1`/{name}`B1`. -/
 noncomputable def redBlock1 (color : Sym2 V → Fin 2) : Finset V :=
   (redNeighbors color).filter (fun v => inBlock1 v)
 
-/-- Red neighbors of `apex` that lie in the second block `{A2,B2}`.
+/-- Red neighbors of {name}`apex` that lie in the second block {name}`A2`/{name}`B2`.
 
-We implement this as the *complement* of `inBlock1` inside `redNeighbors`.
-Since `apex ∉ redNeighbors color`, this is exactly the `{A2,B2}` part. -/
+We implement this as the *complement* of {name}`inBlock1` inside {name}`redNeighbors`.
+Since {name}`apex` is not in {name}`redNeighbors`, this is exactly the {name}`A2`/{name}`B2` part. -/
 noncomputable def redBlock2 (color : Sym2 V → Fin 2) : Finset V :=
   (redNeighbors color).filter (fun v => ¬ inBlock1 v)
 
-/-- Partition of the red neighbors of `apex` into the two blocks. -/
+/-- Partition of the red neighbors of {name}`apex` into the two blocks. -/
 lemma redBlocks_partition_card (color : Sym2 V → Fin 2) :
   (redBlock1 color).card + (redBlock2 color).card = (redNeighbors color).card := by
   classical
@@ -556,7 +560,7 @@ lemma redBlocks_partition_card (color : Sym2 V → Fin 2) :
       (s := redNeighbors color) (p := fun v => inBlock1 v))
 
 /-- **Pigeonhole step.** If there is no blue `K_{1,5}`, then
-one of the two blocks receives at least six red edges from `apex`. -/
+one of the two blocks receives at least six red edges from {name}`apex`. -/
 lemma exists_block_receives_at_least_6_red
     (color : Sym2 V → Fin 2)
     (hNoBlueStar : ¬ hasMonoStar G color 0 5) :
@@ -584,25 +588,25 @@ end PikhurkoN5
 namespace PikhurkoN5
 open V
 
-/-! ## Part / block predicates -/
+/-! # Part / block predicates -/
 
-/-- Recognizes the clique side `A1`. -/
+/-- Recognizes the clique side {name}`A1`. -/
 def isA1 : V → Prop
 | A1 _ => True | _ => False
 
-/-- Recognizes the independent side `B1`. -/
+/-- Recognizes the independent side {name}`B1`. -/
 def isB1 : V → Prop
 | B1 _ => True | _ => False
 
-/-- Recognizes the clique side `A2`. -/
+/-- Recognizes the clique side {name}`A2`. -/
 def isA2 : V → Prop
 | A2 _ => True | _ => False
 
-/-- Recognizes the independent side `B2`. -/
+/-- Recognizes the independent side {name}`B2`. -/
 def isB2 : V → Prop
 | B2 _ => True | _ => False
 
-/-- Second block `{A2,B2}`. -/
+/-- Second block {name}`A2`/{name}`B2`. -/
 def inBlock2 : V → Prop
 | A2 _ => True | B2 _ => True | _ => False
 
@@ -625,27 +629,27 @@ noncomputable instance : DecidablePred inBlock2 := by intro v; cases v <;> infer
 @[simp] lemma not_isA2_and_isB2 (v : V) : ¬ (isA2 v ∧ isB2 v) := by
   cases v <;> simp [isA2, isB2]
 
-/-! ## Splitting the `apex` red neighbors by parts -/
+/-! # Splitting the {name}`apex` red neighbors by parts -/
 
 -- These came from the previous step you have:
 -- def redNeighbors (color : Sym2 V → Fin 2) : Finset V := ...
 
 
-/-- Further refine `redBlock1` into its `A1` and `B1` parts. -/
+/-- Further refine {name}`redBlock1` into its {name}`A1` and {name}`B1` parts. -/
 noncomputable def redBlock1A1 (color : Sym2 V → Fin 2) : Finset V :=
   (redNeighbors color).filter (fun v => isA1 v)
 
 noncomputable def redBlock1B1 (color : Sym2 V → Fin 2) : Finset V :=
   (redNeighbors color).filter (fun v => isB1 v)
 
-/-- Further refine `redBlock2` into its `A2` and `B2` parts. -/
+/-- Further refine {name}`redBlock2` into its {name}`A2` and {name}`B2` parts. -/
 noncomputable def redBlock2A2 (color : Sym2 V → Fin 2) : Finset V :=
   (redNeighbors color).filter (fun v => isA2 v)
 
 noncomputable def redBlock2B2 (color : Sym2 V → Fin 2) : Finset V :=
   (redNeighbors color).filter (fun v => isB2 v)
 
-/-- `redBlock1` is exactly the disjoint union of its `A1` and `B1` parts. -/
+/-- {name}`redBlock1` is exactly the disjoint union of its {name}`A1` and {name}`B1` parts. -/
 lemma redBlock1_eq_union (color : Sym2 V → Fin 2) :
   redBlock1 color =
     redBlock1A1 color ∪ redBlock1B1 color := by
@@ -663,7 +667,7 @@ lemma redBlock1_eq_union (color : Sym2 V → Fin 2) :
     · rcases Finset.mem_filter.1 hB1 with ⟨hRN, hB1⟩
       exact Finset.mem_filter.2 ⟨hRN, (inBlock1_iff v).2 (Or.inr hB1)⟩
 
-/-- `redBlock2` is exactly the disjoint union of its `A2` and `B2` parts. -/
+/-- {name}`redBlock2` is exactly the disjoint union of its {name}`A2` and {name}`B2` parts. -/
 lemma redBlock2_eq_union (color : Sym2 V → Fin 2) :
   redBlock2 color =
     redBlock2A2 color ∪ redBlock2B2 color := by
@@ -687,7 +691,7 @@ lemma redBlock2_eq_union (color : Sym2 V → Fin 2) :
       exact Finset.mem_filter.2 ⟨hRN, by
         cases v <;> simp_all [inBlock1, isB2]⟩
 
-/-- The two parts of `redBlock1` are disjoint. -/
+/-- The two parts of {name}`redBlock1` are disjoint. -/
 lemma redA1_redB1_disjoint (color : Sym2 V → Fin 2) :
   Disjoint (redBlock1A1 color) (redBlock1B1 color) := by
   classical
@@ -697,7 +701,7 @@ lemma redA1_redB1_disjoint (color : Sym2 V → Fin 2) :
   rcases Finset.mem_filter.1 hvB with ⟨_, hB1⟩
   exact (not_isA1_and_isB1 v) ⟨hA1, hB1⟩
 
-/-- The two parts of `redBlock2` are disjoint. -/
+/-- The two parts of {name}`redBlock2` are disjoint. -/
 lemma redA2_redB2_disjoint (color : Sym2 V → Fin 2) :
   Disjoint (redBlock2A2 color) (redBlock2B2 color) := by
   classical
@@ -745,12 +749,12 @@ lemma redBlock2_card_eq_sum (color : Sym2 V → Fin 2) :
   have := by simpa [hU, hI, add_comm] using this
   exact this
 
-/-! ## Bounding the `B`-parts by `5` -/
+/-! # Bounding the {lit}`B`-parts by {lean}`5` -/
 
-/-- All `B1`-vertices as a finset (image of `Fin 5`). -/
+/-- All {name}`B1`-vertices as a finset (image of {lean}`Fin 5`). -/
 def B1Set : Finset V := (Finset.univ.image fun j : Fin 5 => B1 j)
 
-/-- All `B2`-vertices as a finset (image of `Fin 5`). -/
+/-- All {name}`B2`-vertices as a finset (image of {lean}`Fin 5`). -/
 def B2Set : Finset V := (Finset.univ.image fun j : Fin 5 => B2 j)
 
 lemma redBlock1B1_subset_B1Set (color : Sym2 V → Fin 2) :
@@ -799,9 +803,9 @@ lemma redBlock2B2_card_le_5 (color : Sym2 V → Fin 2) :
   (redBlock2B2 color).card ≤ 5 :=
   (Finset.card_le_card (redBlock2B2_subset_B2Set color)).trans card_B2Set_le_5
 
-/-! ## Existence of a red neighbor in the clique parts `A1` / `A2` -/
+/-! # Existence of a red neighbor in the clique parts {name}`A1` / {name}`A2` -/
 
-/-- If block 1 receives at least 6 red neighbors from `apex`, then one of them lies in `A1`. -/
+/-- If block 1 receives at least 6 red neighbors from {name}`apex`, then one of them lies in {name}`A1`. -/
 lemma exists_red_A1_of_block1_ge6
     (color : Sym2 V → Fin 2)
     (h6 : 6 ≤ (redBlock1 color).card) :
@@ -833,7 +837,7 @@ lemma exists_red_A1_of_block1_ge6
   | B2 _ => cases hA1
   | apex  => cases hA1
 
-/-- If block 2 receives at least 6 red neighbors from `apex`, then one of them lies in `A2`. -/
+/-- If block 2 receives at least 6 red neighbors from {name}`apex`, then one of them lies in {name}`A2`. -/
 lemma exists_red_A2_of_block2_ge6
     (color : Sym2 V → Fin 2)
     (h6 : 6 ≤ (redBlock2 color).card) :
@@ -859,8 +863,8 @@ lemma exists_red_A2_of_block2_ge6
   | B2 _ => cases hA2
   | apex  => cases hA2
 
-/-- Corollary: under the “no blue star” hypothesis, there is a red neighbor of `apex`
-in the appropriate clique `A1` or `A2`. -/
+/-- Corollary: under the “no blue star” hypothesis, there is a red neighbor of {name}`apex`
+in the appropriate clique {name}`A1` or {name}`A2`. -/
 lemma exists_red_clique_neighbor
     (color : Sym2 V → Fin 2)
     (hNoBlueStar : ¬ hasMonoStar G color 0 5) :
@@ -881,7 +885,7 @@ end PikhurkoN5
 namespace PikhurkoN5
 open V
 
-/-! ### Helpers: the chosen clique vertex lies in the corresponding red block -/
+/-! # Helpers: the chosen clique vertex lies in the corresponding red block -/
 
 lemma A1_mem_redBlock1_of_red
     (color : Sym2 V → Fin 2) (i : Fin 2)
@@ -911,10 +915,10 @@ lemma A2_mem_redBlock2_of_red
   have hB : inBlock2 (A2 i) := by simp [inBlock2]
   simp [redBlock2, hRN, isA1, isB1]
 
-/-! ### Triangle-or-star from Block 1 -/
+/-! # Triangle-or-star from Block 1 -/
 
-/-- If Block 1 has at least 6 red apex-neighbors, and one of them is `A1 i` with a red edge
-from `apex`, then either we have a red triangle, or a blue `K_{1,5}` centered at `A1 i`. -/
+/-- If Block 1 has at least 6 red apex-neighbors, and one of them is {lean}`A1 i` with a red edge
+from {name}`apex`, then either we have a red triangle, or a blue `K_{1,5}` centered at {lean}`A1 i`. -/
 lemma triangle_or_blueStar_from_block1
     (color : Sym2 V → Fin 2)
     (h6 : 6 ≤ (redBlock1 color).card)
@@ -1011,7 +1015,7 @@ lemma triangle_or_blueStar_from_block1
     intro y hy
     exact ⟨hAdjAll hy, hAllBlue hy⟩
 
-/-! ### Triangle-or-star from Block 2 (same proof pattern) -/
+/-! # Triangle-or-star from Block 2 (same proof pattern) -/
 
 lemma triangle_or_blueStar_from_block2
     (color : Sym2 V → Fin 2)
@@ -1088,7 +1092,7 @@ lemma triangle_or_blueStar_from_block2
     intro y hy
     exact ⟨hAdjAll hy, hAllBlue hy⟩
 
-/-! ### Final step: no blue K_{1,5} ⇒ a red triangle -/
+/-! # Final step: no blue `K_{1,5}` ⇒ a red triangle -/
 
 /-- **Main step (n=5):** If there is no blue `K_{1,5}`, then the red color class contains a triangle. -/
 theorem red_triangle_of_no_blue_star
diff --git a/analysis/Analysis/Misc/erdos_707.lean b/Analysis/Misc/erdos_707.lean
similarity index 94%
rename from analysis/Analysis/Misc/erdos_707.lean
rename to Analysis/Misc/erdos_707.lean
index 28861aae..e5af795d 100644
--- a/analysis/Analysis/Misc/erdos_707.lean
+++ b/Analysis/Misc/erdos_707.lean
@@ -129,11 +129,19 @@ lemma diff_uniq {a b c d:B} (ha: a ≠ b) (hsub: a.val-b.val = c.val-d.val) : a=
   replace : (⟨ a, b ⟩: B × B) = ⟨ c, d ⟩ := by apply this.unique <;> grind
   grind
 
-/-- Given a perfect difference set `B` and an element `a` not in `B`, the function `f_a` maps each `b ∈ B` to the unique `c ∈ B` such that `a-b=c-d` for some `d ∈ B`. -/
+/--
+{given -show}`b, c, d`
+Given a perfect difference set {name}`B` and an element {name}`a` not in {name}`B`, the function
+{lean}`f (a := a)` maps each {lean}`b ∈ B` to the unique {lean}`c ∈ B` such that {lean}`a - b = c -
+d` for some {lean}`d ∈ B`.
+-/
 noncomputable def f {a:ZMod N} (ha: a ∉ B) (b:B): B :=
     (hdiff (a-b.val) (by grind)).choose.1
 
-/-- Though not defined in Theorem 8, it is convenient to also introduce the companion function `g_a`, defined to be the `d` element. -/
+/--
+{given -show}`d`
+Though not defined in Theorem 8, it is convenient to also introduce the companion function {lean}`g (a := a)`, defined to be the {name}`d` element such that {lean}`a - b = f (a := a) ha b - d`.
+-/
 noncomputable def g {a:ZMod N} (ha: a ∉ B) (b:B): B :=
     (hdiff (a-b.val) (by grind)).choose.2
 
@@ -150,7 +158,7 @@ lemma f_def' {a:ZMod N} (ha: a ∉ B) (b c d:B) : a - b = c - d ↔ c = f ha b 
   rintro ⟨ rfl, rfl ⟩
   exact f_def ha b
 
-/-- `f_a` is an involution. -/
+/-- {lean}`f (a := a)` is an involution. -/
 lemma f_inv {a:ZMod N} (ha: a ∉ B) : Function.Involutive (f ha) := by
   intro b
   have h1 := f_def ha b
@@ -158,7 +166,7 @@ lemma f_inv {a:ZMod N} (ha: a ∉ B) : Function.Involutive (f ha) := by
   rw [f_def' ha] at h1
   rw [←h1.1]
 
-/-- Fixed points of `f_a` satisfy `2f_a(b) = a + g_a(b)`. -/
+/-- Fixed points of {lean}`f (a := a)` satisfy {lean}`2 * f ha b = a + g ha b`. -/
 lemma f_fixed {a:ZMod N} {ha: a ∉ B} {b:B} (hb: f ha b = b): 2 * b.val = a + (g ha b).val := by
   have := f_def ha b
   grind
diff --git a/analysis/Analysis/Misc/erdos_987.lean b/Analysis/Misc/erdos_987.lean
similarity index 100%
rename from analysis/Analysis/Misc/erdos_987.lean
rename to Analysis/Misc/erdos_987.lean
diff --git a/analysis/Analysis/Section_10_1.lean b/Analysis/Section_10_1.lean
similarity index 95%
rename from analysis/Analysis/Section_10_1.lean
rename to Analysis/Section_10_1.lean
index ab0ac5c6..a07d0ec8 100644
--- a/analysis/Analysis/Section_10_1.lean
+++ b/Analysis/Section_10_1.lean
@@ -1,6 +1,5 @@
 import Mathlib.Tactic
 import Mathlib.Analysis.Calculus.Deriv.Basic
-
 /-!
 # Analysis I, Section 10.1: Basic definitions
 
@@ -11,12 +10,12 @@ the Lean code could be "golfed" to be more elegant and idiomatic, but I have con
 doing so.
 
 Main constructions and results of this section:
-- API for Mathlib's `HasDerivWithinAt`, `derivWithin`, and `DifferentiableWithinAt`.
+- API for Mathlib's {name}`HasDerivWithinAt`, {name}`derivWithin`, and {name}`DifferentiableWithinAt`.
 
 Note that the Mathlib conventions differ slightly from that in the text, in that
 differentiability is defined even at points that are not limit points of the domain;
-derivatives in such cases may not be unique, but `derivWithin` still selects one such
-derivative in such cases (or `0`, if no derivative exists).
+derivatives in such cases may not be unique, but {name}`derivWithin` still selects one such
+derivative in such cases (or {lean}`0`, if no derivative exists).
 
 -/
 
@@ -24,8 +23,8 @@ namespace Chapter10
 
 variable (x₀ : ℝ)
 
-/-- Definition 10.1.1 (Differentiability at a point).  For the Mathlib notion `HasDerivWithinAt`, the
-hypothesis that `x₀` is a limit point is not needed. -/
+/-- Definition 10.1.1 (Differentiability at a point).  For the Mathlib notion {name}`HasDerivWithinAt`, the
+hypothesis that {name}`x₀` is a limit point is not needed. -/
 theorem _root_.HasDerivWithinAt.iff (X: Set ℝ) (x₀ : ℝ) (f: ℝ → ℝ)
   (L:ℝ) :
   HasDerivWithinAt f L X x₀ ↔ (nhdsWithin x₀ (X \ {x₀})).Tendsto (fun x ↦ (f x - f x₀) / (x - x₀))
diff --git a/analysis/Analysis/Section_10_2.lean b/Analysis/Section_10_2.lean
similarity index 99%
rename from analysis/Analysis/Section_10_2.lean
rename to Analysis/Section_10_2.lean
index 226344b1..bf87cf2e 100644
--- a/analysis/Analysis/Section_10_2.lean
+++ b/Analysis/Section_10_2.lean
@@ -1,6 +1,5 @@
 import Mathlib.Tactic
 import Analysis.Section_9_6
-
 /-!
 # Analysis I, Section 10.2: Local maxima, local minima, and derivatives
 
@@ -20,7 +19,7 @@ Main constructions and results of this section:
 open Chapter9
 namespace Chapter10
 
-/-- Definition 10.2.1 (Local maxima and minima).  Here we use Mathlib's `IsLocalMaxOn` type. -/
+/-- Definition 10.2.1 (Local maxima and minima).  Here we use Mathlib's {name}`IsLocalMaxOn` type. -/
 theorem IsLocalMaxOn.iff (X:Set ℝ) (f:ℝ → ℝ) (x₀:ℝ) :
   IsLocalMaxOn f X x₀ ↔
   ∃ δ > 0, IsMaxOn f (X ∩ .Ioo (x₀ - δ) (x₀ + δ)) x₀ := by
diff --git a/analysis/Analysis/Section_10_3.lean b/Analysis/Section_10_3.lean
similarity index 100%
rename from analysis/Analysis/Section_10_3.lean
rename to Analysis/Section_10_3.lean
diff --git a/analysis/Analysis/Section_10_4.lean b/Analysis/Section_10_4.lean
similarity index 100%
rename from analysis/Analysis/Section_10_4.lean
rename to Analysis/Section_10_4.lean
diff --git a/analysis/Analysis/Section_10_5.lean b/Analysis/Section_10_5.lean
similarity index 100%
rename from analysis/Analysis/Section_10_5.lean
rename to Analysis/Section_10_5.lean
diff --git a/analysis/Analysis/Section_11_1.lean b/Analysis/Section_11_1.lean
similarity index 99%
rename from analysis/Analysis/Section_11_1.lean
rename to Analysis/Section_11_1.lean
index 8cc39957..c5cc328d 100644
--- a/analysis/Analysis/Section_11_1.lean
+++ b/Analysis/Section_11_1.lean
@@ -45,7 +45,7 @@ theorem BoundedInterval.coe_empty : ((∅ : BoundedInterval):Set ℝ) = ∅ := b
   simp [toSet]
 
 open Classical in
-/-- This is to make Finsets of BoundedIntervals work properly -/
+/-- This is to make {name}`Finset`s of {name}`BoundedInterval`s work properly -/
 noncomputable instance BoundedInterval.decidableEq : DecidableEq BoundedInterval := instDecidableEqOfLawfulBEq
 
 @[simp]
diff --git a/analysis/Analysis/Section_11_10.lean b/Analysis/Section_11_10.lean
similarity index 99%
rename from analysis/Analysis/Section_11_10.lean
rename to Analysis/Section_11_10.lean
index 07356d59..45e6d8d4 100644
--- a/analysis/Analysis/Section_11_10.lean
+++ b/Analysis/Section_11_10.lean
@@ -31,7 +31,7 @@ theorem integ_of_mul_deriv {a b:ℝ} (hab: a ≤ b) {F G: ℝ → ℝ}
     integ (G * derivWithin F (Icc a b)) (Icc a b) := by
     sorry
 
-/-- Theorem 11.10.2.  Need to add continuity of α due to our conventions on α-length -/
+/-- Theorem 11.10.2.  Need to add continuity of α due to our conventions on {name}`α_length` -/
 theorem PiecewiseConstantOn.RS_integ_eq_integ_of_mul_deriv
   {a b:ℝ} {α f:ℝ → ℝ}
   (hα_diff: DifferentiableOn ℝ α (Icc a b)) (hαcont: Continuous α)
diff --git a/analysis/Analysis/Section_11_2.lean b/Analysis/Section_11_2.lean
similarity index 99%
rename from analysis/Analysis/Section_11_2.lean
rename to Analysis/Section_11_2.lean
index 5953497f..a9d11ce2 100644
--- a/analysis/Analysis/Section_11_2.lean
+++ b/Analysis/Section_11_2.lean
@@ -155,7 +155,7 @@ theorem PiecewiseConstantOn.smul {f: ℝ → ℝ} {I: BoundedInterval}
   (c:ℝ) (hf: PiecewiseConstantOn f I) : PiecewiseConstantOn (c • f) I := by
   sorry
 
-/-- Lemma 11.2.8 / Exercise 11.2.2.  I believe the hypothesis that `g` does not vanish is not needed. -/
+/-- Lemma 11.2.8 / Exercise 11.2.2.  I believe the hypothesis that {name}`g` does not vanish is not needed. -/
 theorem PiecewiseConstantOn.div {f g: ℝ → ℝ} {I: BoundedInterval}
   (hf: PiecewiseConstantOn f I) (hg: PiecewiseConstantOn f I) : PiecewiseConstantOn (f / g) I := by
   sorry
diff --git a/analysis/Analysis/Section_11_3.lean b/Analysis/Section_11_3.lean
similarity index 94%
rename from analysis/Analysis/Section_11_3.lean
rename to Analysis/Section_11_3.lean
index bb48a711..fb2251ad 100644
--- a/analysis/Analysis/Section_11_3.lean
+++ b/Analysis/Section_11_3.lean
@@ -81,32 +81,30 @@ lemma integral_bound_above {f:ℝ → ℝ} {I: BoundedInterval} (h: BddOn f I) :
 /-- Lemma 11.3.3.  The proof has been reorganized somewhat from the textbook. -/
 lemma le_lower_integral {f:ℝ → ℝ} {I: BoundedInterval} {M:ℝ} (h: ∀ x ∈ (I:Set ℝ), |f x| ≤ M) :
   -M * |I|ₗ ≤ lower_integral f I :=
-  ConditionallyCompleteLattice.le_csSup _ _
-    (integral_bound_above (BddOn.of_bounded h)) (integral_bound_lower_of_bounded h)
+  le_csSup (integral_bound_above (BddOn.of_bounded h)) (integral_bound_lower_of_bounded h)
 
 lemma lower_integral_le_upper {f:ℝ → ℝ} {I: BoundedInterval} (h: BddOn f I) :
   lower_integral f I ≤ upper_integral f I := by
-  apply ConditionallyCompleteLattice.csSup_le _ _ (integral_bound_lower_nonempty h) _
-  rw [mem_upperBounds]; intros
-  apply ConditionallyCompleteLattice.le_csInf _ _ (integral_bound_upper_nonempty h) _
-  rw [mem_lowerBounds]
+  apply csSup_le (integral_bound_lower_nonempty h)
+  intros
+  apply le_csInf (integral_bound_upper_nonempty h)
+  intros
   solve_by_elim [integral_bound_lower_le_upper]
 
 lemma upper_integral_le {f:ℝ → ℝ} {I: BoundedInterval} {M:ℝ} (h: ∀ x ∈ (I:Set ℝ), |f x| ≤ M) :
   upper_integral f I ≤ M * |I|ₗ :=
-  ConditionallyCompleteLattice.csInf_le _ _
-    (integral_bound_below (BddOn.of_bounded h)) (integral_bound_upper_of_bounded h)
+  csInf_le (integral_bound_below (BddOn.of_bounded h)) (integral_bound_upper_of_bounded h)
 
 lemma upper_integral_le_integ {f g:ℝ → ℝ} {I: BoundedInterval} (hf: BddOn f I)
   (hfg: MajorizesOn g f I) (hg: PiecewiseConstantOn g I) :
   upper_integral f I ≤ hg.integ' := by
-  apply ConditionallyCompleteLattice.csInf_le _ _ (integral_bound_below hf) _
+  apply csInf_le (integral_bound_below hf) _
   use g; simpa [hg]
 
 lemma integ_le_lower_integral {f h:ℝ → ℝ} {I: BoundedInterval} (hf: BddOn f I)
   (hfh: MinorizesOn h f I) (hg: PiecewiseConstantOn h I) :
   hg.integ' ≤ lower_integral f I := by
-  apply ConditionallyCompleteLattice.le_csSup _ _ (integral_bound_above hf) _
+  apply le_csSup (integral_bound_above hf) _
   use h; simpa [hg]
 
 lemma lt_of_gt_upper_integral {f:ℝ → ℝ} {I: BoundedInterval} (hf: BddOn f I)
diff --git a/analysis/Analysis/Section_11_4.lean b/Analysis/Section_11_4.lean
similarity index 100%
rename from analysis/Analysis/Section_11_4.lean
rename to Analysis/Section_11_4.lean
diff --git a/analysis/Analysis/Section_11_5.lean b/Analysis/Section_11_5.lean
similarity index 100%
rename from analysis/Analysis/Section_11_5.lean
rename to Analysis/Section_11_5.lean
diff --git a/analysis/Analysis/Section_11_6.lean b/Analysis/Section_11_6.lean
similarity index 100%
rename from analysis/Analysis/Section_11_6.lean
rename to Analysis/Section_11_6.lean
diff --git a/analysis/Analysis/Section_11_7.lean b/Analysis/Section_11_7.lean
similarity index 100%
rename from analysis/Analysis/Section_11_7.lean
rename to Analysis/Section_11_7.lean
diff --git a/analysis/Analysis/Section_11_8.lean b/Analysis/Section_11_8.lean
similarity index 93%
rename from analysis/Analysis/Section_11_8.lean
rename to Analysis/Section_11_8.lean
index 2fc73d57..b9cfb985 100644
--- a/analysis/Analysis/Section_11_8.lean
+++ b/Analysis/Section_11_8.lean
@@ -2,6 +2,8 @@ import Mathlib.Tactic
 import Mathlib.Topology.Instances.Irrational
 import Analysis.Section_11_6
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 11.8: The Riemann-Stieltjes integral
 
@@ -12,22 +14,24 @@ Lean code could be "golfed" to be more elegant and idiomatic, but I have conscio
 doing so.
 
 Main constructions and results of this section:
-- Definition of α-length.
+- Definition of `α_length`.
 - The piecewise constant Riemann-Stieltjes integral.
 - The full Riemann-Stieltjes integral.
 
+{open Set}
+
 Technical notes:
-- In Lean it is more convenient to make definitions such as α-length and the Riemann-Stieltjes
+- In Lean it is more convenient to make definitions such as `α_length` and the Riemann-Stieltjes
   integral totally defined, thus assigning "junk" values to the cases where the definition is
-  not intended to be applied. For the definition of α-length, the definition is intended to be
+  not intended to be applied. For the definition of `α_length`, the definition is intended to be
   applied in contexts where left and right limits exist, and the function is extended by
   constants to the left and right of its intended domain of definition; for instance, if a
-  function `f` is defined on `Icc 0 1`, then it is intended that `f x = f 1` for all `x ≥ 1`
+  function `x` `f` is defined on {lean}`Icc 0 1`, then it is intended that `f x = f 1` for all `x ≥ 1`
   and `f x = f 0` for all `x ≤ 0`; in particular, at a right endpoint, the value of a function
   is intended to agree with its right limit, and similarly for the left endpoint, although we
-  do not enforce this in our definition of α-length. (For functions defined on open intervals,
+  do not enforce this in our definition of `α_length`. (For functions defined on open intervals,
   the extension is immaterial.)
-- The notion of α-length and piecewise constant Riemann-Stieltjes integral is intended for
+- The notion of `α_length` and piecewise constant Riemann-Stieltjes integral is intended for
   situations where left and right limits exist, such as for monotone functions or continuous
   functions, though technically they make sense without these hypotheses. The full Riemann-Stieltjes
   integral is intended for functions that are of bounded variation, though we shall restrict
@@ -39,16 +43,18 @@ namespace Chapter11
 open BoundedInterval Chapter9
 
 /-- Left and right limits. A junk value is assigned if the limit does not exist. -/
-noncomputable abbrev right_lim (f: ℝ → ℝ) (x₀:ℝ) : ℝ := lim ((nhdsWithin x₀ (.Ioi x₀)).map f)
+noncomputable abbrev right_lim (f: ℝ → ℝ) (x₀:ℝ) : ℝ := Filter.lim ((nhdsWithin x₀ (.Ioi x₀)).map f)
 
-noncomputable abbrev left_lim (f: ℝ → ℝ) (x₀:ℝ) : ℝ := lim ((nhdsWithin x₀ (.Iio x₀)).map f)
+noncomputable abbrev left_lim (f: ℝ → ℝ) (x₀:ℝ) : ℝ := Filter.lim ((nhdsWithin x₀ (.Iio x₀)).map f)
 
 theorem right_lim_def {f: ℝ → ℝ} {x₀ L:ℝ} (h: Convergesto (.Ioi x₀) f L x₀) :
   right_lim f x₀ = L := by
+  show Filter.lim _ = L
   apply lim_eq; rwa [Convergesto.iff, Filter.Tendsto.eq_1] at h
 
 theorem left_lim_def {f: ℝ → ℝ} {x₀ L:ℝ} (h: Convergesto (.Iio x₀) f L x₀) :
   left_lim f x₀ = L := by
+  show Filter.lim _ = L
   apply lim_eq; rwa [Convergesto.iff, Filter.Tendsto.eq_1] at h
 
 noncomputable abbrev jump (f: ℝ → ℝ) (x₀:ℝ) : ℝ :=
@@ -135,11 +141,11 @@ theorem right_lim_le_left_lim_of_monotone {f:ℝ → ℝ} {a b:ℝ} (hab: a < b)
   rw [left_lim_of_monotone' b hf, right_lim_of_monotone' a hf]
   calc
     _ ≤ f ((a+b)/2) := by
-      apply ConditionallyCompleteLattice.csInf_le
+      apply csInf_le
       . rw [bddBelow_def]; use f a; intro y hy; simp at hy; obtain ⟨ x, hx, rfl ⟩ := hy; apply hf; grind
       simp; use (a+b)/2; simp; linarith
     _ ≤ _ := by
-      apply ConditionallyCompleteLattice.le_csSup
+      apply le_csSup
       . rw [bddAbove_def]; use f b; intro y hy; simp at hy; obtain ⟨ x, hx, rfl ⟩ := hy; apply hf; grind
       simp; use (a+b)/2; simp; linarith
 
@@ -150,7 +156,8 @@ noncomputable abbrev α_length (α: ℝ → ℝ) (I: BoundedInterval) : ℝ := m
 | Ioc a b => if a ≤ b then (right_lim α b) - (right_lim α a) else 0
 | Ioo a b => if a < b then (left_lim α b) - (right_lim α a) else 0
 
-notation3:max α"["I"]ₗ" => α_length α I
+syntax:max term "[" term "]ₗ" : term
+macro_rules | `($α[$I]ₗ) => `(α_length $α $I)
 
 theorem α_length_of_empty (α: ℝ → ℝ) {I: BoundedInterval} (hI: (I:Set ℝ) = ∅) : α[I]ₗ = 0 :=
   match I with
@@ -199,7 +206,7 @@ example : (fun x ↦ x^2)[Ioo 2 2]ₗ = 0 := by
 theorem α_len_of_id (I: BoundedInterval) : (fun x ↦ x)[I]ₗ = |I|ₗ := by
   sorry
 
-/-- An improved version of BoundedInterval.joins that also controls α-length. -/
+/-- An improved version of {name}`BoundedInterval.joins` that also controls {name}`α_length`. -/
 abbrev BoundedInterval.joins' (K I J: BoundedInterval) : Prop :=  K.joins I J ∧ ∀ α:ℝ → ℝ, α[K]ₗ = α[I]ₗ + α[J]ₗ
 
 theorem BoundedInterval.join_Icc_Ioc' {a b c:ℝ} (hab: a ≤ b) (hbc: b ≤ c) : (Icc a c).joins' (Icc a b) (Ioc b c) := ⟨ join_Icc_Ioc hab hbc,
@@ -264,7 +271,7 @@ theorem PiecewiseConstantOn.RS_integ_def {f:ℝ → ℝ} {I: BoundedInterval} {P
   have h' : PiecewiseConstantOn f I := by use P
   simp [RS_integ, h']; exact PiecewiseConstantWith.RS_integ_eq h'.choose_spec h α
 
-/-- α-length non-negative when α monotone -/
+/-- {name}`α_length` non-negative when α monotone -/
 theorem α_length_nonneg_of_monotone {α:ℝ → ℝ}  (hα: Monotone α) (I: BoundedInterval):
   0 ≤ α[I]ₗ := by
   sorry
@@ -392,34 +399,32 @@ lemma RS_integral_bound_above {f:ℝ → ℝ} {I: BoundedInterval} (h: BddOn f I
 lemma le_lower_RS_integral {f:ℝ → ℝ} {I: BoundedInterval} {M:ℝ} (h: ∀ x ∈ (I:Set ℝ), |f x| ≤ M)
   {α:ℝ → ℝ} (hα: Monotone α) :
   -M * α[I]ₗ ≤ lower_RS_integral f I α :=
-  ConditionallyCompleteLattice.le_csSup _ _
-    (RS_integral_bound_above (BddOn.of_bounded h) hα) (RS_integral_bound_lower_of_bounded h hα)
+  le_csSup (RS_integral_bound_above (BddOn.of_bounded h) hα) (RS_integral_bound_lower_of_bounded h hα)
 
 lemma lower_RS_integral_le_upper {f:ℝ → ℝ} {I: BoundedInterval} (h: BddOn f I)
   {α:ℝ → ℝ} (hα: Monotone α) :
   lower_RS_integral f I α ≤ upper_RS_integral f I α := by
-  apply ConditionallyCompleteLattice.csSup_le _ _ (RS_integral_bound_lower_nonempty h hα) _
-  rw [mem_upperBounds]; intros
-  apply ConditionallyCompleteLattice.le_csInf _ _ (RS_integral_bound_upper_nonempty h hα) _
-  rw [mem_lowerBounds]; intros; solve_by_elim [RS_integral_bound_lower_le_upper]
+  apply csSup_le (RS_integral_bound_lower_nonempty h hα)
+  intros
+  apply le_csInf (RS_integral_bound_upper_nonempty h hα)
+  intros; solve_by_elim [RS_integral_bound_lower_le_upper]
 
 lemma RS_upper_integral_le {f:ℝ → ℝ} {I: BoundedInterval} {M:ℝ} (h: ∀ x ∈ (I:Set ℝ), |f x| ≤ M)
   {α:ℝ → ℝ} (hα: Monotone α) :
   upper_RS_integral f I α ≤ M * α[I]ₗ :=
-  ConditionallyCompleteLattice.csInf_le _ _
-    (RS_integral_bound_below (.of_bounded h) hα) (RS_integral_bound_upper_of_bounded h hα)
+  csInf_le (RS_integral_bound_below (.of_bounded h) hα) (RS_integral_bound_upper_of_bounded h hα)
 
 lemma upper_RS_integral_le_integ {f g:ℝ → ℝ} {I: BoundedInterval} (hf: BddOn f I)
   (hfg: MajorizesOn g f I) (hg: PiecewiseConstantOn g I)
   {α:ℝ → ℝ} (hα: Monotone α) :
   upper_RS_integral f I α ≤ PiecewiseConstantOn.RS_integ g I α :=
-  ConditionallyCompleteLattice.csInf_le _ _ (RS_integral_bound_below hf hα) ⟨ g, by simpa [hg] ⟩
+  csInf_le (RS_integral_bound_below hf hα) ⟨ g, by simpa [hg] ⟩
 
 lemma integ_le_lower_RS_integral {f h:ℝ → ℝ} {I: BoundedInterval} (hf: BddOn f I)
   (hfh: MinorizesOn h f I) (hg: PiecewiseConstantOn h I)
   {α:ℝ → ℝ} (hα: Monotone α) :
   PiecewiseConstantOn.RS_integ h I α ≤ lower_RS_integral f I α :=
-  ConditionallyCompleteLattice.le_csSup _ _ (RS_integral_bound_above hf hα) ⟨ h, by simpa [hg] ⟩
+  le_csSup (RS_integral_bound_above hf hα) ⟨ h, by simpa [hg] ⟩
 
 lemma lt_of_gt_upper_RS_integral {f:ℝ → ℝ} {I: BoundedInterval} (hf: BddOn f I)
   {α: ℝ → ℝ} (hα: Monotone α) {X:ℝ} (hX: upper_RS_integral f I α < X ) :
diff --git a/analysis/Analysis/Section_11_9.lean b/Analysis/Section_11_9.lean
similarity index 100%
rename from analysis/Analysis/Section_11_9.lean
rename to Analysis/Section_11_9.lean
diff --git a/analysis/Analysis/Section_2_1.lean b/Analysis/Section_2_1.lean
similarity index 84%
rename from analysis/Analysis/Section_2_1.lean
rename to Analysis/Section_2_1.lean
index 594f8508..7054178a 100644
--- a/analysis/Analysis/Section_2_1.lean
+++ b/Analysis/Section_2_1.lean
@@ -14,7 +14,7 @@ so.
 
 Main constructions and results of this section:
 
-- Definition of the "Chapter 2" natural numbers, `Chapter2.Nat`, abbreviated as `Nat` within the
+- Definition of the "Chapter 2" natural numbers, `Chapter2.Nat`, abbreviated as {name}`Nat` within the
   Chapter2 namespace. (In the book, the natural numbers are treated in a purely axiomatic
   fashion, as a type that obeys the Peano axioms; but here we take advantage of Lean's native
   inductive types to explicitly construct a version of the natural numbers that obey those
@@ -24,7 +24,7 @@ Main constructions and results of this section:
 - Recursive definitions for `Chapter2.Nat`.
 
 Note: at the end of this chapter, the `Chapter2.Nat` class will be deprecated in favor of the
-standard Mathlib class `_root_.Nat`, or `ℕ`.  However, we will develop the properties of
+standard Mathlib class {name}`_root_.Nat`, or {lean}`ℕ`.  However, we will develop the properties of
 `Chapter2.Nat` "by hand" in the next few sections for pedagogical purposes.
 
 -/
@@ -32,8 +32,8 @@ standard Mathlib class `_root_.Nat`, or `ℕ`.  However, we will develop the pro
 namespace Chapter2
 
 /--
-  Assumption 2.6 (Existence of natural numbers).  Here we use an explicit construction of the
-  natural numbers (using an inductive type).  For a more axiomatic approach, see the epilogue to
+  Assumption 2.6 (Existence of natural numbers). Here we use an explicit construction of the
+  natural numbers (using an inductive type). For a more axiomatic approach, see the epilogue to
   this chapter.
 -/
 inductive Nat where
@@ -52,8 +52,8 @@ postfix:100 "++" => Nat.succ
 
 /--
   Definition 2.1.3 (Definition of the numerals 0, 1, 2, etc.). Note: to avoid ambiguity, one may
-  need to use explicit casts such as (0:Nat), (1:Nat), etc. to refer to this chapter's version of
-  the natural numbers.
+  need to use explicit casts such as {lean}`(0:Nat)`, {lean}`(1:Nat)`, etc. to refer to this chapter's version
+  of the natural numbers.
 -/
 instance Nat.instOfNat {n:_root_.Nat} : OfNat Nat n where
   ofNat := _root_.Nat.rec 0 (fun _ n ↦ n++) n
@@ -71,7 +71,7 @@ lemma Nat.two_succ : 2++ = 3 := by rfl
 
 /--
   Axiom 2.3 (0 is not the successor of any natural number).
-  Compare with Lean's `Nat.succ_ne_zero`.
+  Compare with Lean's {name}`Nat.succ_ne_zero`.
 -/
 theorem Nat.succ_ne (n:Nat) : n++ ≠ 0 := by
   by_contra h
@@ -86,14 +86,14 @@ theorem Nat.four_ne : (4:Nat) ≠ 0 := by
 
 /--
   Axiom 2.4 (Different natural numbers have different successors).
-  Compare with Mathlib's `Nat.succ_inj`.
+  Compare with Mathlib's {name}`Nat.succ_inj`.
 -/
 theorem Nat.succ_cancel {n m:Nat} (hnm: n++ = m++) : n = m := by
   injection hnm
 
 /--
   Axiom 2.4 (Different natural numbers have different successors).
-  Compare with Mathlib's `Nat.succ_ne_succ`.
+  Compare with Mathlib's {name}`Nat.succ_ne_succ`.
 -/
 theorem Nat.succ_ne_succ (n m:Nat) : n ≠ m → n++ ≠ m++ := by
   intro h
@@ -111,12 +111,12 @@ theorem Nat.six_ne_two : (6:Nat) ≠ 2 := by
   have := four_ne
   contradiction
 
-/-- One can also prove this sort of result by the `decide` tactic -/
+/-- One can also prove this sort of result by the {tactic}`decide` tactic -/
 theorem Nat.six_ne_two' : (6:Nat) ≠ 2 := by
   decide
 
 /--
-  Axiom 2.5 (Principle of mathematical induction). The `induction` (or `induction'`) tactic in
+  Axiom 2.5 (Principle of mathematical induction). The {tactic}`induction` (or {tactic}`induction'`) tactic in
   Mathlib serves as a substitute for this axiom.
 -/
 theorem Nat.induction (P : Nat → Prop) (hbase : P 0) (hind : ∀ n, P n → P (n++)) :
@@ -127,17 +127,17 @@ theorem Nat.induction (P : Nat → Prop) (hbase : P 0) (hind : ∀ n, P n → P
   | succ n ih => exact hind _ ih
 
 /--
-  Recursion. Analogous to the inbuilt Mathlib method `Nat.rec` associated to
+  Recursion. Analogous to the inbuilt Mathlib method {name}`Nat.rec` associated to
   the Mathlib natural numbers
 -/
 abbrev Nat.recurse (f: Nat → Nat → Nat) (c: Nat) : Nat → Nat := fun n ↦ match n with
 | 0 => c
 | n++ => f n (recurse f c n)
 
-/-- Proposition 2.1.16 (recursive definitions). Compare with Mathlib's `Nat.rec_zero`. -/
+/-- Proposition 2.1.16 (recursive definitions). Compare with Mathlib's {name}`Nat.rec_zero`. -/
 theorem Nat.recurse_zero (f: Nat → Nat → Nat) (c: Nat) : Nat.recurse f c 0 = c := by rfl
 
-/-- Proposition 2.1.16 (recursive definitions). Compare with Mathlib's `Nat.rec_add_one`. -/
+/-- Proposition 2.1.16 (recursive definitions). Compare with Mathlib's {name}`Nat.rec_add_one`. -/
 theorem Nat.recurse_succ (f: Nat → Nat → Nat) (c: Nat) (n: Nat) :
     recurse f c (n++) = f n (recurse f c n) := by rfl
 
diff --git a/analysis/Analysis/Section_2_2.lean b/Analysis/Section_2_2.lean
similarity index 73%
rename from analysis/Analysis/Section_2_2.lean
rename to Analysis/Section_2_2.lean
index 7b01ee60..1709e87c 100644
--- a/analysis/Analysis/Section_2_2.lean
+++ b/Analysis/Section_2_2.lean
@@ -15,12 +15,12 @@ doing so.
 
 Main constructions and results of this section:
 
-- Definition of addition and order for the "Chapter 2" natural numbers, `Chapter2.Nat`.
+- Definition of addition and order for the "Chapter 2" natural numbers, {name}`Chapter2.Nat`.
 - Establishment of basic properties of addition and order.
 
-Note: at the end of this chapter, the `Chapter2.Nat` class will be deprecated in favor of the
-standard Mathlib class `_root_.Nat`, or `ℕ`.  However, we will develop the properties of
-`Chapter2.Nat` "by hand" for pedagogical purposes.
+Note: at the end of this chapter, the {name}`Chapter2.Nat` class will be deprecated in favor of the
+standard Mathlib class {name}`_root_.Nat`, or {lean}`ℕ`.  However, we will develop the properties of
+{name}`Chapter2.Nat` "by hand" for pedagogical purposes.
 
 ## Tips from past users
 
@@ -33,21 +33,21 @@ Users of the companion who have completed the exercises in this section are welc
 namespace Chapter2
 
 /-- Definition 2.2.1. (Addition of natural numbers).
-    Compare with Mathlib's `Nat.add` -/
+    Compare with Mathlib's {name}`Nat.add` -/
 abbrev Nat.add (n m : Nat) : Nat := Nat.recurse (fun _ sum ↦ sum++) m n
 
-/-- This instance allows for the `+` notation to be used for natural number addition. -/
+/-- This instance allows for the {kw (of := «term_+_»)}`+` notation to be used for natural number addition. -/
 instance Nat.instAdd : Add Nat where
   add := add
 
-/-- Compare with Mathlib's `Nat.zero_add`. -/
+/-- Compare with Mathlib's {name}`Nat.zero_add`. -/
 @[simp]
 theorem Nat.zero_add (m: Nat) : 0 + m = m := recurse_zero (fun _ sum ↦ sum++) _
 
-/-- Compare with Mathlib's `Nat.succ_add`. -/
+/-- Compare with Mathlib's {name}`Nat.succ_add`. -/
 theorem Nat.succ_add (n m: Nat) : n++ + m = (n+m)++ := by rfl
 
-/-- Compare with Mathlib's `Nat.one_add`. -/
+/-- Compare with Mathlib's {name}`Nat.one_add`. -/
 theorem Nat.one_add (m:Nat) : 1 + m = m++ := by
   rw [show 1 = 0++ from rfl, succ_add, zero_add]
 
@@ -60,7 +60,7 @@ example : (2:Nat) + 3 = 5 := by
 -- The sum of two natural numbers is again a natural number.
 #check (fun (n m:Nat) ↦ n + m)
 
-/-- Lemma 2.2.2 (n + 0 = n). Compare with Mathlib's `Nat.add_zero`. -/
+/-- Lemma 2.2.2 ({lean}`n + 0 = n`). Compare with Mathlib's {name}`Nat.add_zero`. -/
 @[simp]
 lemma Nat.add_zero (n:Nat) : n + 0 = n := by
   -- This proof is written to follow the structure of the original text.
@@ -71,7 +71,7 @@ lemma Nat.add_zero (n:Nat) : n + 0 = n := by
     (n++) + 0 = (n + 0)++ := by rfl
     _ = n++ := by rw [ih]
 
-/-- Lemma 2.2.3 (n+(m++) = (n+m)++). Compare with Mathlib's `Nat.add_succ`. -/
+/-- Lemma 2.2.3 ({lean}`n+(m++) = (n+m)++`). Compare with Mathlib's {name}`Nat.add_succ`. -/
 lemma Nat.add_succ (n m:Nat) : n + (m++) = (n + m)++ := by
   -- this proof is written to follow the structure of the original text.
   revert n; apply induction
@@ -81,11 +81,11 @@ lemma Nat.add_succ (n m:Nat) : n + (m++) = (n + m)++ := by
   rw [succ_add]
 
 
-/-- n++ = n + 1 (Why?). Compare with Mathlib's `Nat.succ_eq_add_one` -/
+/-- {lean}`n++ = n + 1` (Why?). Compare with Mathlib's {name}`Nat.succ_eq_add_one` -/
 theorem Nat.succ_eq_add_one (n:Nat) : n++ = n + 1 := by
   sorry
 
-/-- Proposition 2.2.4 (Addition is commutative). Compare with Mathlib's `Nat.add_comm` -/
+/-- Proposition 2.2.4 (Addition is commutative). Compare with Mathlib's {name}`Nat.add_comm` -/
 theorem Nat.add_comm (n m:Nat) : n + m = m + n := by
   -- this proof is written to follow the structure of the original text.
   revert n; apply induction
@@ -95,12 +95,12 @@ theorem Nat.add_comm (n m:Nat) : n + m = m + n := by
   rw [add_succ, ih]
 
 /-- Proposition 2.2.5 (Addition is associative) / Exercise 2.2.1
-    Compare with Mathlib's `Nat.add_assoc`. -/
+    Compare with Mathlib's {name}`Nat.add_assoc`. -/
 theorem Nat.add_assoc (a b c:Nat) : (a + b) + c = a + (b + c) := by
   sorry
 
 /-- Proposition 2.2.6 (Cancellation law).
-    Compare with Mathlib's `Nat.add_left_cancel`. -/
+    Compare with Mathlib's {name}`Nat.add_left_cancel`. -/
 theorem Nat.add_left_cancel (a b c:Nat) (habc: a + b = a + c) : b = c := by
   -- This proof is written to follow the structure of the original text.
   revert a; apply induction
@@ -112,8 +112,8 @@ theorem Nat.add_left_cancel (a b c:Nat) (habc: a + b = a + c) : b = c := by
   exact ih hbc
 
 
-/-- (Not from textbook) Nat can be given the structure of a commutative additive monoid.
-This permits tactics such as `abel` to apply to the Chapter 2 natural numbers. -/
+/-- (Not from textbook) {name}`Nat` can be given the structure of a commutative additive monoid.
+This permits tactics such as {tactic}`abel` to apply to the Chapter 2 natural numbers. -/
 instance Nat.addCommMonoid : AddCommMonoid Nat where
   add_assoc := add_assoc
   add_comm := add_comm
@@ -121,7 +121,7 @@ instance Nat.addCommMonoid : AddCommMonoid Nat where
   add_zero := add_zero
   nsmul := nsmulRec
 
-/-- This illustration of the `abel` tactic is not from the
+/-- This illustration of the {tactic}`abel` tactic is not from the
     textbook. -/
 example (a b c d:Nat) : (a+b)+(c+0+d) = (b+c)+(d+a) := by abel
 
@@ -131,7 +131,7 @@ def Nat.IsPos (n:Nat) : Prop := n ≠ 0
 theorem Nat.isPos_iff (n:Nat) : n.IsPos ↔ n ≠ 0 := by rfl
 
 /-- Proposition 2.2.8 (positive plus natural number is positive).
-    Compare with Mathlib's `Nat.add_pos_left`. -/
+    Compare with Mathlib's {name}`Nat.add_pos_left`. -/
 theorem Nat.add_pos_left {a:Nat} (b:Nat) (ha: a.IsPos) : (a + b).IsPos := by
   -- This proof is written to follow the structure of the original text.
   revert b; apply induction
@@ -141,15 +141,15 @@ theorem Nat.add_pos_left {a:Nat} (b:Nat) (ha: a.IsPos) : (a + b).IsPos := by
   have : (a+b)++ ≠ 0 := succ_ne _
   exact this
 
-/-- Compare with Mathlib's `Nat.add_pos_right`.
+/-- Compare with Mathlib's {name}`Nat.add_pos_right`.
 
-This theorem is a consequence of the previous theorem and `add_comm`, and `grind` can automatically discover such proofs.
+This theorem is a consequence of the previous theorem and {name}`add_comm`, and {tactic}`grind` can automatically discover such proofs.
 -/
 theorem Nat.add_pos_right {a:Nat} (b:Nat) (ha: a.IsPos) : (b + a).IsPos := by
   grind [add_comm, add_pos_left]
 
 /-- Corollary 2.2.9 (if sum vanishes, then summands vanish).
-    Compare with Mathlib's `Nat.add_eq_zero`. -/
+    Compare with Mathlib's {name}`Nat.add_eq_zero`. -/
 theorem Nat.add_eq_zero (a b:Nat) (hab: a + b = 0) : a = 0 ∧ b = 0 := by
   -- This proof is written to follow the structure of the original text.
   by_contra h
@@ -176,32 +176,32 @@ lemma Nat.uniq_succ_eq (a:Nat) (ha: a.IsPos) : ∃! b, b++ = a := by
   sorry
 
 /-- Definition 2.2.11 (Ordering of the natural numbers).
-    This defines the `≤` notation on the natural numbers. -/
+    This defines the {kw (of := «term_≤_»)}`≤` notation on the natural numbers. -/
 instance Nat.instLE : LE Nat where
   le n m := ∃ a:Nat, m = n + a
 
 /-- Definition 2.2.11 (Ordering of the natural numbers).
-    This defines the `<` notation on the natural numbers. -/
+    This defines the {kw (of := «term_<_»)}`<` notation on the natural numbers. -/
 instance Nat.instLT : LT Nat where
   lt n m := n ≤ m ∧ n ≠ m
 
-/-- Compare with Mathlib's `le_iff_exists_add`. -/
+/-- Compare with Mathlib's {name}`le_iff_exists_add`. -/
 lemma Nat.le_iff (n m:Nat) : n ≤ m ↔ ∃ a:Nat, m = n + a := by rfl
 
 lemma Nat.lt_iff (n m:Nat) : n < m ↔ (∃ a:Nat, m = n + a) ∧ n ≠ m := by rfl
 
-/-- Compare with Mathlib's `ge_iff_le`. -/
+/-- Compare with Mathlib's {name}`ge_iff_le`. -/
 @[symm]
 lemma Nat.ge_iff_le (n m:Nat) : n ≥ m ↔ m ≤ n := by rfl
 
-/-- Compare with Mathlib's `gt_iff_lt`. -/
+/-- Compare with Mathlib's {name}`gt_iff_lt`. -/
 @[symm]
 lemma Nat.gt_iff_lt (n m:Nat) : n > m ↔ m < n := by rfl
 
-/-- Compare with Mathlib's `Nat.le_of_lt`. -/
+/-- Compare with Mathlib's {name}`Nat.le_of_lt`. -/
 lemma Nat.le_of_lt {n m:Nat} (hnm: n < m) : n ≤ m := hnm.1
 
-/-- Compare with Mathlib's `Nat.le_iff_lt_or_eq`. -/
+/-- Compare with Mathlib's {name}`Nat.le_iff_lt_or_eq`. -/
 lemma Nat.le_iff_lt_or_eq (n m:Nat) : n ≤ m ↔ n < m ∨ n = m := by
   rw [Nat.le_iff, Nat.lt_iff]
   by_cases h : n = m
@@ -218,49 +218,49 @@ example : (8:Nat) > 5 := by
     use 3
   decide
 
-/-- Compare with Mathlib's `Nat.lt_succ_self`. -/
+/-- Compare with Mathlib's {name}`Nat.lt_succ_self`. -/
 theorem Nat.succ_gt_self (n:Nat) : n++ > n := by
   sorry
 
 /-- Proposition 2.2.12 (Basic properties of order for natural numbers) / Exercise 2.2.3
 
-(a) (Order is reflexive). Compare with Mathlib's `Nat.le_refl`.-/
+(a) (Order is reflexive). Compare with Mathlib's {name}`Nat.le_refl`.-/
 theorem Nat.ge_refl (a:Nat) : a ≥ a := by
   sorry
 
 @[refl]
 theorem Nat.le_refl (a:Nat) : a ≤ a := a.ge_refl
 
-/-- The refl tag allows for the `rfl` tactic to work for inequalities. -/
+/-- The refl tag allows for the {tactic}`rfl` tactic to work for inequalities. -/
 example (a b:Nat): a+b ≥ a+b := by rfl
 
-/-- (b) (Order is transitive).  The `obtain` tactic will be useful here.
-    Compare with Mathlib's `Nat.le_trans`. -/
+/-- (b) (Order is transitive).  The {tactic}`obtain` tactic will be useful here.
+    Compare with Mathlib's {name}`Nat.le_trans`. -/
 theorem Nat.ge_trans {a b c:Nat} (hab: a ≥ b) (hbc: b ≥ c) : a ≥ c := by
   sorry
 
 theorem Nat.le_trans {a b c:Nat} (hab: a ≤ b) (hbc: b ≤ c) : a ≤ c := Nat.ge_trans hbc hab
 
-/-- (c) (Order is anti-symmetric). Compare with Mathlib's `Nat.le_antisymm`. -/
+/-- (c) (Order is anti-symmetric). Compare with Mathlib's {name}`Nat.le_antisymm`. -/
 theorem Nat.ge_antisymm {a b:Nat} (hab: a ≥ b) (hba: b ≥ a) : a = b := by
   sorry
 
-/-- (d) (Addition preserves order).  Compare with Mathlib's `Nat.add_le_add_right`. -/
+/-- (d) (Addition preserves order).  Compare with Mathlib's {name}`Nat.add_le_add_right`. -/
 theorem Nat.add_ge_add_right (a b c:Nat) : a ≥ b ↔ a + c ≥ b + c := by
   sorry
 
-/-- (d) (Addition preserves order).  Compare with Mathlib's `Nat.add_le_add_left`.  -/
+/-- (d) (Addition preserves order).  Compare with Mathlib's {name}`Nat.add_le_add_left`.  -/
 theorem Nat.add_ge_add_left (a b c:Nat) : a ≥ b ↔ c + a ≥ c + b := by
   simp only [add_comm]
   exact add_ge_add_right _ _ _
 
-/-- (d) (Addition preserves order).  Compare with Mathlib's `Nat.add_le_add_right`.  -/
+/-- (d) (Addition preserves order).  Compare with Mathlib's {name}`Nat.add_le_add_right`.  -/
 theorem Nat.add_le_add_right (a b c:Nat) : a ≤ b ↔ a + c ≤ b + c := add_ge_add_right _ _ _
 
-/-- (d) (Addition preserves order).  Compare with Mathlib's `Nat.add_le_add_left`.  -/
+/-- (d) (Addition preserves order).  Compare with Mathlib's {name}`Nat.add_le_add_left`.  -/
 theorem Nat.add_le_add_left (a b c:Nat) : a ≤ b ↔ c + a ≤ c + b := add_ge_add_left _ _ _
 
-/-- (e) a < b iff a++ ≤ b.  Compare with Mathlib's `Nat.succ_le_iff`. -/
+/-- (e) a < b iff a++ ≤ b.  Compare with Mathlib's {name}`Nat.succ_le_iff`. -/
 theorem Nat.lt_iff_succ_le (a b:Nat) : a < b ↔ a++ ≤ b := by
   sorry
 
@@ -295,13 +295,13 @@ theorem Nat.lt_of_le_of_lt {a b c : Nat} (hab: a ≤ b) (hbc: b < c) : a < c :=
   . exact add_pos_right d he1
   . rw [he2, hd, add_assoc]
 
-/-- This lemma was a `why?` statement from Proposition 2.2.13,
+/-- This lemma was a {lit}`why?` statement from Proposition 2.2.13,
 but is more broadly useful, so is extracted here. -/
 theorem Nat.zero_le (a:Nat) : 0 ≤ a := by
   sorry
 
 /-- Proposition 2.2.13 (Trichotomy of order for natural numbers) / Exercise 2.2.4
-    Compare with Mathlib's `trichotomous`.  Parts of this theorem have been placed
+    Compare with Mathlib's {name}`trichotomous`.  Parts of this theorem have been placed
     in the preceding Lean theorems. -/
 theorem Nat.trichotomous (a b:Nat) : a < b ∨ a = b ∨ a > b := by
   -- This proof is written to follow the structure of the original text.
@@ -322,11 +322,11 @@ theorem Nat.trichotomous (a b:Nat) : a < b ∨ a = b ∨ a > b := by
 /--
   (Not from textbook) Establish the decidability of this order computably.  The portion of the
   proof involving decidability has been provided; the remaining sorries involve claims about the
-  natural numbers.  One could also have established this result by the `classical` tactic
-  followed by `exact Classical.decRel _`, but this would make this definition (as well as some
+  natural numbers.  One could also have established this result by the {tactic}`classical` tactic
+  followed by {syntax tactic}`exact Classical.decRel _`, but this would make this definition (as well as some
   instances below) noncomputable.
 
-  Compare with Mathlib's `Nat.decLe`.
+  Compare with Mathlib's {name}`Nat.decLe`.
 -/
 def Nat.decLe : (a b : Nat) → Decidable (a ≤ b)
   | 0, b => by
@@ -348,8 +348,8 @@ def Nat.decLe : (a b : Nat) → Decidable (a ≤ b)
 
 instance Nat.decidableRel : DecidableRel (· ≤ · : Nat → Nat → Prop) := Nat.decLe
 
-/-- (Not from textbook) Nat has the structure of a linear ordering. This allows for tactics
-such as `order` and `calc` to be applicable to the Chapter 2 natural numbers. -/
+/-- (Not from textbook) {name}`Nat` has the structure of a linear ordering. This allows for tactics
+such as {tactic}`order` and {tactic}`calc` to be applicable to the Chapter 2 natural numbers. -/
 instance Nat.instLinearOrder : LinearOrder Nat where
   le_refl := ge_refl
   le_trans a b c hab hbc := ge_trans hbc hab
@@ -371,12 +371,12 @@ instance Nat.instLinearOrder : LinearOrder Nat where
     . right; exact le_of_lt h
   toDecidableLE := decidableRel
 
-/-- This illustration of the `order` tactic is not from the
+/-- This illustration of the {tactic}`order` tactic is not from the
     textbook. -/
 example (a b c d:Nat) (hab: a ≤ b) (hbc: b ≤ c) (hcd: c ≤ d)
         (hda: d ≤ a) : a = c := by order
 
-/-- An illustration of the `calc` tactic with `≤/<`. -/
+/-- An illustration of the {tactic}`calc` tactic with {kw (of := «term_≤_»)}`≤`/{kw (of := «term_<_»)}`<`. -/
 example (a b c d e:Nat) (hab: a ≤ b) (hbc: b < c) (hcd: c ≤ d)
         (hde: d ≤ e) : a + 0 < e := by
   calc
@@ -386,12 +386,12 @@ example (a b c d e:Nat) (hab: a ≤ b) (hbc: b < c) (hcd: c ≤ d)
         _ ≤ d := hcd
         _ ≤ e := hde
 
-/-- (Not from textbook) Nat has the structure of an ordered monoid. This allows for tactics
-such as `gcongr` to be applicable to the Chapter 2 natural numbers. -/
+/-- (Not from textbook) {name}`Nat` has the structure of an ordered monoid. This allows for tactics
+such as {tactic}`gcongr` to be applicable to the Chapter 2 natural numbers. -/
 instance Nat.isOrderedAddMonoid : IsOrderedAddMonoid Nat where
   add_le_add_left a b hab c := (Nat.add_le_add_right a b c).mp hab
 
-/-- This illustration of the `gcongr` tactic is not from the
+/-- This illustration of the {tactic}`gcongr` tactic is not from the
     textbook. -/
 example (a b c d e:Nat) (hab: a ≤ b) (hbc: b < c) (hde: d < e) :
   a + d ≤ c + e := by
@@ -399,7 +399,7 @@ example (a b c d e:Nat) (hab: a ≤ b) (hbc: b < c) (hde: d < e) :
   order
 
 /-- Proposition 2.2.14 (Strong principle of induction) / Exercise 2.2.5
-    Compare with Mathlib's `Nat.strong_induction_on`.
+    Compare with Mathlib's {name}`Nat.strong_induction_on`.
 -/
 theorem Nat.strong_induction {m₀:Nat} {P: Nat → Prop}
   (hind: ∀ m, m ≥ m₀ → (∀ m', m₀ ≤ m' ∧ m' < m → P m') → P m) :
@@ -407,14 +407,14 @@ theorem Nat.strong_induction {m₀:Nat} {P: Nat → Prop}
   sorry
 
 /-- Exercise 2.2.6 (backwards induction)
-    Compare with Mathlib's `Nat.decreasingInduction`. -/
+    Compare with Mathlib's {name}`Nat.decreasingInduction`. -/
 theorem Nat.backwards_induction {n:Nat} {P: Nat → Prop}
   (hind: ∀ m, P (m++) → P m) (hn: P n) :
     ∀ m, m ≤ n → P m := by
   sorry
 
 /-- Exercise 2.2.7 (induction from a starting point)
-    Compare with Mathlib's `Nat.le_induction`. -/
+    Compare with Mathlib's {name}`Nat.le_induction`. -/
 theorem Nat.induction_from {n:Nat} {P: Nat → Prop} (hind: ∀ m, P m → P (m++)) :
     P n → ∀ m, m ≥ n → P m := by
   sorry
diff --git a/analysis/Analysis/Section_2_3.lean b/Analysis/Section_2_3.lean
similarity index 77%
rename from analysis/Analysis/Section_2_3.lean
rename to Analysis/Section_2_3.lean
index bc15c6be..aa322e4b 100644
--- a/analysis/Analysis/Section_2_3.lean
+++ b/Analysis/Section_2_3.lean
@@ -16,11 +16,11 @@ doing so.
 Main constructions and results of this section:
 
 - Definition of multiplication and exponentiation for the "Chapter 2" natural numbers,
-  `Chapter2.Nat`.
+  {name}`Chapter2.Nat`.
 
-Note: at the end of this chapter, the `Chapter2.Nat` class will be deprecated in favor of the
-standard Mathlib class `_root_.Nat`, or `ℕ`.  However, we will develop the properties of
-`Chapter2.Nat` "by hand" for pedagogical purposes.
+Note: at the end of this chapter, the {name}`Chapter2.Nat` class will be deprecated in favor of the
+standard Mathlib class {name}`_root_.Nat`, or {lean}`ℕ`.  However, we will develop the properties of
+{name}`Chapter2.Nat` "by hand" for pedagogical purposes.
 
 ## Tips from past users
 
@@ -35,22 +35,22 @@ namespace Chapter2
 /-- Definition 2.3.1 (Multiplication of natural numbers) -/
 abbrev Nat.mul (n m : Nat) : Nat := Nat.recurse (fun _ prod ↦ prod + m) 0 n
 
-/-- This instance allows for the `*` notation to be used for natural number multiplication. -/
+/-- This instance allows for the {kw (of := «term_*_»)}`*` notation to be used for natural number multiplication. -/
 instance Nat.instMul : Mul Nat where
   mul := mul
 
 /-- Definition 2.3.1 (Multiplication of natural numbers)
-Compare with Mathlib's `Nat.zero_mul` -/
+Compare with Mathlib's {name}`Nat.zero_mul` -/
 theorem Nat.zero_mul (m: Nat) : 0 * m = 0 := recurse_zero (fun _ prod ↦ prod+m) _
 
 /-- Definition 2.3.1 (Multiplication of natural numbers)
-Compare with Mathlib's `Nat.succ_mul` -/
+Compare with Mathlib's {name}`Nat.succ_mul` -/
 theorem Nat.succ_mul (n m: Nat) : (n++) * m = n * m + m := recurse_succ (fun _ prod ↦ prod+m) _ _
 
 theorem Nat.one_mul' (m: Nat) : 1 * m = 0 + m := by
   rw [←zero_succ, succ_mul, zero_mul]
 
-/-- Compare with Mathlib's `Nat.one_mul` -/
+/-- Compare with Mathlib's {name}`Nat.one_mul` -/
 theorem Nat.one_mul (m: Nat) : 1 * m = m := by
   rw [one_mul', zero_add]
 
@@ -58,36 +58,36 @@ theorem Nat.two_mul (m: Nat) : 2 * m = 0 + m + m := by
   rw [←one_succ, succ_mul, one_mul']
 
 /-- This lemma will be useful to prove Lemma 2.3.2.
-Compare with Mathlib's `Nat.mul_zero` -/
+Compare with Mathlib's {name}`Nat.mul_zero` -/
 lemma Nat.mul_zero (n: Nat) : n * 0 = 0 := by
   sorry
 
 /-- This lemma will be useful to prove Lemma 2.3.2.
-Compare with Mathlib's `Nat.mul_succ` -/
+Compare with Mathlib's {name}`Nat.mul_succ` -/
 lemma Nat.mul_succ (n m:Nat) : n * m++ = n * m + n := by
   sorry
 
 /-- Lemma 2.3.2 (Multiplication is commutative) / Exercise 2.3.1
-Compare with Mathlib's `Nat.mul_comm` -/
+Compare with Mathlib's {name}`Nat.mul_comm` -/
 lemma Nat.mul_comm (n m: Nat) : n * m = m * n := by
   sorry
 
-/-- Compare with Mathlib's `Nat.mul_one` -/
+/-- Compare with Mathlib's {name}`Nat.mul_one` -/
 theorem Nat.mul_one (m: Nat) : m * 1 = m := by
   rw [mul_comm, one_mul]
 
 /-- This lemma will be useful to prove Lemma 2.3.3.
-Compare with Mathlib's `Nat.mul_pos` -/
+Compare with Mathlib's {name}`Nat.mul_pos` -/
 lemma Nat.pos_mul_pos {n m: Nat} (h₁: n.IsPos) (h₂: m.IsPos) : (n * m).IsPos := by
   sorry
 
 /-- Lemma 2.3.3 (Positive natural numbers have no zero divisors) / Exercise 2.3.2.
-    Compare with Mathlib's `Nat.mul_eq_zero`.  -/
+    Compare with Mathlib's {name}`Nat.mul_eq_zero`.  -/
 lemma Nat.mul_eq_zero (n m: Nat) : n * m = 0 ↔ n = 0 ∨ m = 0 := by
   sorry
 
 /-- Proposition 2.3.4 (Distributive law)
-Compare with Mathlib's `Nat.mul_add` -/
+Compare with Mathlib's {name}`Nat.mul_add` -/
 theorem Nat.mul_add (a b c: Nat) : a * (b + c) = a * b + a * c := by
   -- This proof is written to follow the structure of the original text.
   revert c; apply induction
@@ -98,17 +98,17 @@ theorem Nat.mul_add (a b c: Nat) : a * (b + c) = a * b + a * c := by
   rw [mul_succ, ←add_assoc, ←habc]
 
 /-- Proposition 2.3.4 (Distributive law)
-Compare with Mathlib's `Nat.add_mul`  -/
+Compare with Mathlib's {name}`Nat.add_mul`  -/
 theorem Nat.add_mul (a b c: Nat) : (a + b)*c = a*c + b*c := by
   simp only [mul_comm, mul_add]
 
 /-- Proposition 2.3.5 (Multiplication is associative) / Exercise 2.3.3
-Compare with Mathlib's `Nat.mul_assoc` -/
+Compare with Mathlib's {name}`Nat.mul_assoc` -/
 theorem Nat.mul_assoc (a b c: Nat) : (a * b) * c = a * (b * c) := by
   sorry
 
-/-- (Not from textbook)  Nat is a commutative semiring.
-    This allows tactics such as `ring` to apply to the Chapter 2 natural numbers. -/
+/-- (Not from textbook)  {name}`Nat` is a commutative semiring.
+    This allows tactics such as {tactic}`ring` to apply to the Chapter 2 natural numbers. -/
 instance Nat.instCommSemiring : CommSemiring Nat where
   left_distrib := mul_add
   right_distrib := add_mul
@@ -119,13 +119,13 @@ instance Nat.instCommSemiring : CommSemiring Nat where
   mul_one := mul_one
   mul_comm := mul_comm
 
-/-- This illustration of the `ring` tactic is not from the
+/-- This illustration of the {tactic}`ring` tactic is not from the
     textbook. -/
 example (a b c d:ℕ) : (a+b)*1*(c+d) = d*b+a*c+c*b+a*d+0 := by ring
 
 
 /-- Proposition 2.3.6 (Multiplication preserves order)
-Compare with Mathlib's `Nat.mul_lt_mul_of_pos_right` -/
+Compare with Mathlib's {name}`Nat.mul_lt_mul_of_pos_right` -/
 theorem Nat.mul_lt_mul_of_pos_right {a b c: Nat} (h: a < b) (hc: c.IsPos) : a * c < b * c := by
   -- This proof is written to follow the structure of the original text.
   rw [lt_iff_add_pos] at h
@@ -141,7 +141,7 @@ theorem Nat.mul_gt_mul_of_pos_right {a b c: Nat} (h: a > b) (hc: c.IsPos) :
     a * c > b * c := mul_lt_mul_of_pos_right h hc
 
 /-- Proposition 2.3.6 (Multiplication preserves order)
-Compare with Mathlib's `Nat.mul_lt_mul_of_pos_left` -/
+Compare with Mathlib's {name}`Nat.mul_lt_mul_of_pos_left` -/
 theorem Nat.mul_lt_mul_of_pos_left {a b c: Nat} (h: a < b) (hc: c.IsPos) : c * a < c * b := by
   simp [mul_comm]
   exact mul_lt_mul_of_pos_right h hc
@@ -151,7 +151,7 @@ theorem Nat.mul_gt_mul_of_pos_left {a b c: Nat} (h: a > b) (hc: c.IsPos) :
     c * a > c * b := mul_lt_mul_of_pos_left h hc
 
 /-- Corollary 2.3.7 (Cancellation law)
-Compare with Mathlib's `Nat.mul_right_cancel` -/
+Compare with Mathlib's {name}`Nat.mul_right_cancel` -/
 lemma Nat.mul_cancel_right {a b c: Nat} (h: a * c = b * c) (hc: c.IsPos) : a = b := by
   -- This proof is written to follow the structure of the original text.
   have := trichotomous a b
@@ -164,14 +164,14 @@ lemma Nat.mul_cancel_right {a b c: Nat} (h: a * c = b * c) (hc: c.IsPos) : a = b
   apply ne_of_gt at hgt
   contradiction
 
-/-- (Not from textbook) Nat is an ordered semiring.
-This allows tactics such as `gcongr` to apply to the Chapter 2 natural numbers. -/
+/-- (Not from textbook) {name}`Nat` is an ordered semiring.
+This allows tactics such as {tactic}`gcongr` to apply to the Chapter 2 natural numbers. -/
 instance Nat.isOrderedRing : IsOrderedRing Nat where
   zero_le_one := by sorry
   mul_le_mul_of_nonneg_left := by sorry
   mul_le_mul_of_nonneg_right := by sorry
 
-/-- This illustration of the `gcongr` tactic is not from the
+/-- This illustration of the {tactic}`gcongr` tactic is not from the
     textbook. -/
 example (a b c d:Nat) (hab: a ≤ b) : c*a*d ≤ c*b*d := by
   gcongr
@@ -179,7 +179,7 @@ example (a b c d:Nat) (hab: a ≤ b) : c*a*d ≤ c*b*d := by
   exact c.zero_le
 
 /-- Proposition 2.3.9 (Euclid's division lemma) / Exercise 2.3.5
-Compare with Mathlib's `Nat.mod_eq_iff` -/
+Compare with Mathlib's {name}`Nat.mod_eq_iff` -/
 theorem Nat.exists_div_mod (n:Nat) {q: Nat} (hq: q.IsPos) :
     ∃ m r: Nat, 0 ≤ r ∧ r < q ∧ n = m * q + r := by
   sorry
@@ -191,7 +191,7 @@ instance Nat.instPow : HomogeneousPow Nat where
   pow := Nat.pow
 
 /-- Definition 2.3.11 (Exponentiation for natural numbers)
-Compare with Mathlib's `Nat.pow_zero` -/
+Compare with Mathlib's {name}`Nat.pow_zero` -/
 @[simp]
 theorem Nat.pow_zero (m: Nat) : m ^ (0:Nat) = 1 := recurse_zero (fun _ prod ↦ prod * m) _
 
@@ -200,11 +200,11 @@ theorem Nat.pow_zero (m: Nat) : m ^ (0:Nat) = 1 := recurse_zero (fun _ prod ↦
 theorem Nat.zero_pow_zero : (0:Nat) ^ 0 = 1 := recurse_zero (fun _ prod ↦ prod * 0) _
 
 /-- Definition 2.3.11 (Exponentiation for natural numbers)
-Compare with Mathlib's `Nat.pow_succ` -/
+Compare with Mathlib's {name}`Nat.pow_succ` -/
 theorem Nat.pow_succ (m n: Nat) : (m:Nat) ^ n++ = m^n * m :=
   recurse_succ (fun _ prod ↦ prod * m) _ _
 
-/-- Compare with Mathlib's `Nat.pow_one` -/
+/-- Compare with Mathlib's {name}`Nat.pow_one` -/
 @[simp]
 theorem Nat.pow_one (m: Nat) : m ^ (1:Nat) = m := by
   rw [←zero_succ, pow_succ]; simp
diff --git a/analysis/Analysis/Section_2_epilogue.lean b/Analysis/Section_2_epilogue.lean
similarity index 78%
rename from analysis/Analysis/Section_2_epilogue.lean
rename to Analysis/Section_2_epilogue.lean
index 844eb33e..f06aebd7 100644
--- a/analysis/Analysis/Section_2_epilogue.lean
+++ b/Analysis/Section_2_epilogue.lean
@@ -4,20 +4,20 @@ import Analysis.Section_2_3
 /-!
 # Analysis I, Chapter 2 epilogue: Isomorphism with the Mathlib natural numbers
 
-In this (technical) epilogue, we show that the "Chapter 2" natural numbers `Chapter2.Nat` are
-isomorphic in various senses to the standard natural numbers `ℕ`.
+In this (technical) epilogue, we show that the "Chapter 2" natural numbers {name}`Chapter2.Nat` are
+isomorphic in various senses to the standard natural numbers {lean}`ℕ`.
 
-After this epilogue, `Chapter2.Nat` will be deprecated, and we will instead use the standard
-natural numbers `ℕ` throughout.  In particular, one should use the full Mathlib API for `ℕ` for
-all subsequent chapters, in lieu of the `Chapter2.Nat` API.
+After this epilogue, {name}`Chapter2.Nat` will be deprecated, and we will instead use the standard
+natural numbers {lean}`ℕ` throughout.  In particular, one should use the full Mathlib API for {lean}`ℕ` for
+all subsequent chapters, in lieu of the {name}`Chapter2.Nat` API.
 
-Filling the sorries here requires both the Chapter2.Nat API and the Mathlib API for the standard
-natural numbers `ℕ`.  As such, they are excellent exercises to prepare you for the aforementioned
+Filling the sorries here requires both the {name}`Chapter2.Nat` API and the Mathlib API for the standard
+natural numbers {lean}`ℕ`.  As such, they are excellent exercises to prepare you for the aforementioned
 transition.
 
 In second half of this section we also give a fully axiomatic treatment of the natural numbers
 via the Peano axioms. The treatment in the preceding three sections was only partially axiomatic,
-because we used a specific construction `Chapter2.Nat` of the natural numbers that was an inductive
+because we used a specific construction {name}`Chapter2.Nat` of the natural numbers that was an inductive
 type, and used that inductive type to construct a recursor.  Here, we give some exercises to show
 how one can accomplish the same tasks directly from the Peano axioms, without knowing the specific
 implementation of the natural numbers.
@@ -81,7 +81,7 @@ lemma Chapter2.Nat.pow_eq_pow (n m : Chapter2.Nat) :
   sorry
 
 
-/-- The Peano axioms for an abstract type `Nat` -/
+/-- The Peano axioms for an abstract type {name}`Nat` -/
 @[ext]
 structure PeanoAxioms where
   Nat : Type
@@ -117,37 +117,37 @@ abbrev natCast (P : PeanoAxioms) : ℕ → P.Nat := fun n ↦ match n with
   | Nat.zero => P.zero
   | Nat.succ n => P.succ (natCast P n)
 
-/-- One can start the proof here with `unfold Function.Injective`, although it is not strictly necessary. -/
+/-- One can start the proof here with {syntax tactic}`unfold Function.Injective`, although it is not strictly necessary. -/
 theorem natCast_injective (P : PeanoAxioms) : Function.Injective P.natCast := by
   sorry
 
-/-- One can start the proof here with `unfold Function.Surjective`, although it is not strictly necessary. -/
+/-- One can start the proof here with {syntax tactic}`unfold Function.Surjective`, although it is not strictly necessary. -/
 theorem natCast_surjective (P : PeanoAxioms) : Function.Surjective P.natCast := by
   sorry
 
 /-- The notion of an equivalence between two structures obeying the Peano axioms.
-    The symbol `≃` is an alias for Mathlib's `Equiv` class; for instance `P.Nat ≃ Q.Nat` is
-    an alias for `_root_.Equiv P.Nat Q.Nat`. -/
+    The symbol {kw (of := «term_≃_»)}`≃` is an alias for Mathlib's {name}`Equiv` class; for instance {lean}`P.Nat ≃ Q.Nat` is
+    an alias for {lean}`_root_.Equiv P.Nat Q.Nat`. -/
 class Equiv (P Q : PeanoAxioms) where
   equiv : P.Nat ≃ Q.Nat
   equiv_zero : equiv P.zero = Q.zero
   equiv_succ : ∀ n : P.Nat, equiv (P.succ n) = Q.succ (equiv n)
 
-/-- This exercise will require application of Mathlib's API for the `Equiv` class.
-    Some of this API can be invoked automatically via the `simp` tactic. -/
+/-- This exercise will require application of Mathlib's API for the {name}`Equiv` class.
+    Some of this API can be invoked automatically via the {tactic}`simp` tactic. -/
 abbrev Equiv.symm {P Q: PeanoAxioms} (equiv : Equiv P Q) : Equiv Q P where
   equiv := equiv.equiv.symm
   equiv_zero := by sorry
   equiv_succ n := by sorry
 
-/-- This exercise will require application of Mathlib's API for the `Equiv` class.
-    Some of this API can be invoked automatically via the `simp` tactic. -/
+/-- This exercise will require application of Mathlib's API for the {name}`Equiv` class.
+    Some of this API can be invoked automatically via the {tactic}`simp` tactic. -/
 abbrev Equiv.trans {P Q R: PeanoAxioms} (equiv1 : Equiv P Q) (equiv2 : Equiv Q R) : Equiv P R where
   equiv := equiv1.equiv.trans equiv2.equiv
   equiv_zero := by sorry
   equiv_succ n := by sorry
 
-/-- Useful Mathlib tools for inverting bijections include `Function.surjInv` and `Function.invFun`. -/
+/-- Useful Mathlib tools for inverting bijections include {name}`Function.surjInv` and {name}`Function.invFun`. -/
 noncomputable abbrev Equiv.fromNat (P : PeanoAxioms) : Equiv Mathlib_Nat P where
   equiv := {
     toFun := P.natCast
diff --git a/analysis/Analysis/Section_3_1.lean b/Analysis/Section_3_1.lean
similarity index 92%
rename from analysis/Analysis/Section_3_1.lean
rename to Analysis/Section_3_1.lean
index b317b779..cf81c741 100644
--- a/analysis/Analysis/Section_3_1.lean
+++ b/Analysis/Section_3_1.lean
@@ -1,5 +1,7 @@
 import Mathlib.Tactic
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 3.1: Fundamentals (of set theory)
 
@@ -18,9 +20,9 @@ Main constructions and results of this section:
 - A type `Chapter3.SetTheory.Set` of sets
 - A type `Chapter3.SetTheory.Object` of objects
 - An axiom that every set is (or can be coerced into) an object
-- The empty set `∅`, singletons `{y}`, and pairs `{y,z}` (and more general finite tuples), with
+- The empty set {syntax term}`∅`, singletons {syntax term}`{y}`, and pairs {syntax term}`{y,z}` (and more general finite tuples), with
   their attendant axioms
-- Pairwise union `X ∪ Y`, and their attendant axioms
+- Pairwise union {syntax term}`X ∪ Y`, and their attendant axioms
 - Coercion of a set `A` to its associated type `A.toSubtype`, which is a subtype of `Object`, and
   basic API.  (This is a technical construction needed to make the Zermelo-Frankel set theory
   compatible with the dependent type theory of Lean.)
@@ -34,15 +36,15 @@ Main constructions and results of this section:
   `Chapter3.Nat : Chapter3.Set` (the axiom of infinity).
 - Axioms of regularity, power set, and union (used in later sections of this chapter, but not
   required here)
-- Connections with Mathlib's notion of a set
+- Connections with Mathlib's notion of a {name}`Set`
 
 The other axioms of Zermelo-Frankel set theory are discussed in later sections.
 
 Some technical notes:
-- Mathlib of course has its own notion of a `Set` (or more precisely, a type `Set X` associated to
+- Mathlib of course has its own notion of a {name}`Set` (or more precisely, a type `Set X` associated to
   each type `X`), which is not compatible with the notion `Chapter3.Set` defined here,
   though we will try to make the notations match as much as possible.  This causes some notational
-  conflict: for instance, one may need to explicitly specify `(∅:Chapter3.Set)` instead of just `∅`
+  conflict: for instance, one may need to explicitly specify `(∅:Chapter3.Set)` instead of just {syntax term}`∅`
   to indicate that one is using the `Chapter3.Set` version of the empty set, rather than the
   Mathlib version of the empty set, and similarly for other notation defined here.
 - In Analysis I, we chose to work with an "impure" set theory, in which there could be more
@@ -54,12 +56,13 @@ Some technical notes:
   specifically to a subtype of `Object`.  A similar coercion is in place for Mathlib's
   formalization of sets.
 - After this chapter is concluded, the notion of a `Chapter3.SetTheory.Set` will be deprecated in
-  favor of the standard Mathlib notion of a `Set` (or more precisely of the type `Set X` of a set
+  favor of the standard Mathlib notion of a {name}`Set` (or more precisely of the type `Set X` of a set
   in a given type `X`).  However, due to various technical incompatibilities between set theory
   and type theory, we will not attempt to create a full equivalence between these two
   notions of sets. (As such, this makes this entire chapter optional from the point of view of
   the rest of the book, though we retain it for pedagogical purposes.)
 
+
 ## Tips from past users
 
 Users of the companion who have completed the exercises in this section are welcome to send their tips for future users in this section as PRs.
@@ -73,7 +76,7 @@ namespace Chapter3
 becomes relevant when constructing models of set theory in the Chapter 3 epilogue. -/
 universe u v
 
-/-- The axioms of Zermelo-Frankel theory with atoms.  -/
+/-- The axioms of Zermelo-Frankel theory with atoms. -/
 class SetTheory where
   Set : Type u -- Axiom 3.1
   Object : Type v -- Axiom 3.1
@@ -135,7 +138,7 @@ theorem SetTheory.Set.coe_eq {X Y:Set} (h: (X: Object) = (Y: Object)) : X = Y :=
 theorem SetTheory.Set.coe_eq_iff (X Y:Set) : (X: Object) = (Y: Object) ↔  X = Y :=
   ⟨ coe_eq, by rintro rfl; rfl ⟩
 
-/-- Axiom 3.2 (Equality of sets).  The `[ext]` tag allows the `ext` tactic to work for sets. -/
+/-- Axiom 3.2 (Equality of sets).  The {attr}`@[ext]` tag allows the {tactic}`ext` tactic to work for sets. -/
 @[ext]
 theorem SetTheory.Set.ext {X Y:Set} (h: ∀ x, x ∈ X ↔ x ∈ Y) : X = Y := extensionality _ _ h
 
@@ -153,7 +156,7 @@ open SetTheory.Set
 
 /--
   Axiom 3.3 (empty set).
-  Note: in some applications one may have to explicitly cast ∅ to Set due to
+  Note: in some applications one may have to explicitly cast {lean}`(∅ : Set)` to {name}`Set` due to
   Mathlib's existing set theory notation.
 -/
 @[simp]
@@ -188,7 +191,7 @@ example (x: Object) : {x} = SetTheory.singleton x := rfl
 
 /--
   Axiom 3.3(a) (singleton).
-  Note: in some applications one may have to explicitly cast {a} to Set due to Mathlib's
+  Note: in some applications one may have to explicitly cast {lean (type := "Set")}`{a}` to {name}`Set` due to Mathlib's
   existing set theory notation.
 -/
 @[simp]
@@ -213,12 +216,12 @@ instance SetTheory.Set.instInsert : Insert Object Set where
 theorem SetTheory.Set.mem_insert (a b: Object) (X: Set) : a ∈ insert b X ↔ a = b ∨ a ∈ X := by
   simp only [insert, Insert.insert, mem_union, mem_singleton]
 
-/-- Axiom 3.3(b) (pair).  Note: in some applications one may have to cast {a,b}
-    to Set. -/
+/-- Axiom 3.3(b) (pair).  Note: in some applications one may have to cast {lean (type := "Set")}`{a,b}`
+    to {name}`Set`. -/
 theorem SetTheory.Set.pair_eq (a b:Object) : ({a,b}:Set) = {a} ∪ {b} := by rfl
 
-/-- Axiom 3.3(b) (pair).  Note: in some applications one may have to cast {a,b}
-    to Set. -/
+/-- Axiom 3.3(b) (pair).  Note: in some applications one may have to cast {lean (type := "Set")}`{a,b}`
+    to {name}`Set`. -/
 @[simp]
 theorem SetTheory.Set.mem_pair (x a b:Object) : x ∈ ({a,b}:Set) ↔ (x = a ∨ x = b) := by
   simp [pair_eq, mem_union, mem_singleton]
@@ -329,12 +332,12 @@ example (X Y: Set) : X ⊆ Y ↔ ∀ x, x ∈ X → x ∈ Y := by rfl
 
 /--
   Definition 3.1.14.
-  Note that the strict subset operation in Mathlib is denoted `⊂` rather than `⊊`.
+  Note that the strict subset operation in Mathlib is denoted {kw (of := «term_⊂_»)}`⊂` rather than `⊊`.
 -/
 instance SetTheory.Set.instSSubset : HasSSubset Set where
   SSubset X Y := X ⊆ Y ∧ X ≠ Y
 
--- Now we can use `⊂` for a strict subset relationship between two `Set`s.
+/-- Now we can use {kw (of := «term_⊂_»)}`⊂` for a strict subset relationship between two {name}`Set`s. -/
 example (X Y: Set) : X ⊂ Y ↔ X ⊆ Y ∧ X ≠ Y := by rfl
 
 /-- Definition 3.1.14. -/
@@ -342,7 +345,7 @@ theorem SetTheory.Set.subset_def (X Y:Set) : X ⊆ Y ↔ ∀ x, x ∈ X → x 
 
 /--
   Definition 3.1.14.
-  Note that the strict subset operation in Mathlib is denoted `⊂` rather than `⊊`.
+  Note that the strict subset operation in Mathlib is denoted {kw (of := «term_⊂_»)}`⊂` rather than `⊊`.
 -/
 theorem SetTheory.Set.ssubset_def (X Y:Set) : X ⊂ Y ↔ (X ⊆ Y ∧ X ≠ Y) := by rfl
 
@@ -377,13 +380,13 @@ theorem SetTheory.Set.ssubset_trans (A B C:Set) (hAB:A ⊂ B) (hBC:B ⊂ C) : A
 
 
 /--
-  This defines the subtype `A.toSubtype` for any `A:Set`.
-  Note that `A.toSubtype` gives you a type, similar to how `Object` or `Set` are types.
-  A value `x'` of type `A.toSubtype` combines some `x: Object` with a proof that `hx: x ∈ A`.
+  This defines the subtype {lean}`A.toSubtype` for any {lean}`A:Set`.
+  Note that {lean}`A.toSubtype` gives you a type, similar to how {name}`Object` or {name}`Set` are types.
+  A value {given (type := "A.toSubtype")}`x'` of type {lean}`A.toSubtype` combines some {given}`x: Object` with a proof that {given}`hx: x ∈ A`.
 
-  To produce an element `x'` of this subtype, use `⟨ x, hx ⟩`, where `x: Object` and `hx: x ∈ A`.
-  The object `x` associated to a subtype element `x'` is recovered as `x'.val`, and
-  the property `hx` that `x` belongs to `A` is recovered as `x'.property`.
+  To produce an element {name}`x'` of this subtype, use {lean (type := "A.toSubtype")}`⟨ x, hx ⟩`, where {lean}`x: Object` and {lean}`hx: x ∈ A`.
+  The object {name}`x` associated to a subtype element {name}`x'` is recovered as {lean}`x'.val`, and
+  the property {name}`hx` that {name}`x` belongs to {name}`A` is recovered as {lean}`x'.property`.
 -/
 abbrev SetTheory.Set.toSubtype (A:Set) := Subtype (fun x ↦ x ∈ A)
 
@@ -416,8 +419,8 @@ lemma SetTheory.Set.subtype_coe (A:Set) (x:A) : x.val = x := rfl
 lemma SetTheory.Set.coe_inj (A:Set) (x y:A) : x.val = y.val ↔ x = y := Subtype.coe_inj
 
 /--
-  If one has a proof `hx` of `x ∈ A`, then `A.subtype_mk hx` will then make the element of `A`
-  (viewed as a subtype) corresponding to `x`.
+  If one has a proof {name}`hx` of {lean}`x ∈ A`, then {lean}`A.subtype_mk hx` will then make the element of {name}`A`
+  (viewed as a subtype) corresponding to {name}`x`.
 -/
 def SetTheory.Set.subtype_mk (A:Set) {x:Object} (hx:x ∈ A) : A := ⟨ x, hx ⟩
 
@@ -730,7 +733,7 @@ example : ({3,5,9}:Set).replace (P := fun x y ↦ ∃ (n:ℕ), x.val = n ∧ y =
 example : ({3,5,9}:Set).replace (P := fun _ y ↦ y=1) (by aesop) = {1} := by
   ext; simp only [replacement_axiom]; aesop
 
-/-- Exercise 3.1.5.  One can use the `tfae_have` and `tfae_finish` tactics here. -/
+/-- Exercise 3.1.5.  One can use the {tactic}`tfae_have` and {tactic}`tfae_finish` tactics here. -/
 theorem SetTheory.Set.subset_tfae (A B:Set) : [A ⊆ B, A ∪ B = B, A ∩ B = A].TFAE := by sorry
 
 /-- Exercise 3.1.7 -/
@@ -778,7 +781,7 @@ theorem SetTheory.Set.partition_right {A B X:Set} (h_union: A ∪ B = X) (h_inte
 
 /--
   Exercise 3.1.10.
-  You may find `Function.onFun_apply` and the `fin_cases` tactic useful.
+  You may find {name}`Function.onFun_apply` and the {tactic}`fin_cases` tactic useful.
 -/
 theorem SetTheory.Set.pairwise_disjoint (A B:Set) :
     Pairwise (Function.onFun Disjoint ![A \ B, A ∩ B, B \ A]) := by sorry
@@ -789,8 +792,8 @@ theorem SetTheory.Set.union_eq_partition (A B:Set) : A ∪ B = (A \ B) ∪ (A 
 
 /--
   Exercise 3.1.11.
-  The challenge is to prove this without using `Set.specify`, `Set.specification_axiom`,
-  `Set.specification_axiom'`, or anything built from them (like differences and intersections).
+  The challenge is to prove this without using {name}`Set.specify`, {name}`Set.specification_axiom`,
+  {name}`Set.specification_axiom'`, or anything built from them (like differences and intersections).
 -/
 theorem SetTheory.Set.specification_from_replacement {A:Set} {P: A → Prop} :
     ∃ B, B ⊆ A ∧ ∀ x, x.val ∈ B ↔ P x := by sorry
@@ -840,7 +843,7 @@ theorem SetTheory.Set.coe_inj' (X Y:Set) :
     replace h := congr(x ∈ $h); simpa using h
   rintro rfl; rfl
 
-/-- Compatibility of the membership operation ∈ -/
+/-- Compatibility of the membership operation {kw (of := «term_∈_»)}`∈` -/
 theorem SetTheory.Set.mem_coe (X:Set) (x:Object) : x ∈ (X : _root_.Set Object) ↔ x ∈ X := by
   simp
 
diff --git a/analysis/Analysis/Section_3_2.lean b/Analysis/Section_3_2.lean
similarity index 100%
rename from analysis/Analysis/Section_3_2.lean
rename to Analysis/Section_3_2.lean
diff --git a/analysis/Analysis/Section_3_3.lean b/Analysis/Section_3_3.lean
similarity index 92%
rename from analysis/Analysis/Section_3_3.lean
rename to Analysis/Section_3_3.lean
index 37ecc3d1..c7af01a4 100644
--- a/analysis/Analysis/Section_3_3.lean
+++ b/Analysis/Section_3_3.lean
@@ -2,6 +2,8 @@ import Mathlib.Tactic
 import Analysis.Section_3_1
 import Analysis.Tools.ExistsUnique
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 3.3: Functions
 
@@ -22,12 +24,12 @@ Main constructions and results of this section:
 
 In the rest of the book we will deprecate the Chapter 3 version of a function, and work with the
 Mathlib notion of a function instead.  Even within this section, we will switch to the Mathlib
-formalism for some of the examples involving number systems such as `ℤ` or `ℝ` that have not been
+formalism for some of the examples involving number systems such as {lean}`ℤ` or {lean}`ℝ` that have not been
 implemented in the Chapter 3 framework.
 
-We will work here with the version `Nat` of the natural numbers internal to the Chapter 3 set
+We will work here with the version {name}`Nat` of the natural numbers internal to the Chapter 3 set
 theory, though usually we will use coercions to then immediately translate to the Mathlib
-natural numbers `ℕ`.
+natural numbers {lean}`ℕ`.
 
 ## Tips from past users
 
@@ -45,8 +47,8 @@ export SetTheory (Set Object)
 variable [SetTheory]
 
 /--
-  Definition 3.3.1. `Function X Y` is the structure of functions from `X` to `Y`.
-  Analogous to the Mathlib type `X → Y`.
+  Definition 3.3.1. {lean}`Function X Y` is the structure of functions from {lean}`X` to {lean}`Y`.
+  Analogous to the Mathlib type {lean}`X → Y`.
 -/
 @[ext]
 structure Function (X Y: Set) where
@@ -56,7 +58,7 @@ structure Function (X Y: Set) where
 #check Function.mk
 
 /--
-  Converting a Chapter 3 function `f: Function X Y` to a Mathlib function `f: X → Y`.
+  Converting a Chapter 3 function {lean}`f: Function X Y` to a Mathlib function {lean}`f: X → Y`.
   The Chapter 3 definition of a function was nonconstructive, so we have to use the
   axiom of choice here.
 -/
@@ -68,7 +70,7 @@ noncomputable instance Function.inst_coefn (X Y: Set) : CoeFun (Function X Y) (f
 
 theorem Function.to_fn_eval {X Y: Set} (f: Function X Y) (x:X) : f.to_fn x = f x := rfl
 
-/-- Converting a Mathlib function to a Chapter 3 `Function` -/
+/-- Converting a Mathlib function to a Chapter 3 {name}`Function` -/
 abbrev Function.mk_fn {X Y: Set} (f: X → Y) : Function X Y :=
   Function.mk (fun x y ↦ y = f x) (by simp)
 
@@ -135,7 +137,7 @@ abbrev SetTheory.Set.f_3_3_3c : Function (Nat \ {(0:Object)}: Set) Nat :=
 theorem SetTheory.Set.f_3_3_3c_eval (x: (Nat \ {(0:Object)}: Set)) (y: Nat) :
     y = f_3_3_3c x ↔ ((y+1:ℕ):Object) = x := Function.eval _ _ _
 
-/-- Create a version of a non-zero `n` inside `Nat \ {0}` for any natural number n. -/
+/-- Create a version of a non-zero {lean}`n` inside {lean}`Nat \ {0}` for any natural number n. -/
 abbrev SetTheory.Set.coe_nonzero (n:ℕ) (h: n ≠ 0): (Nat \ {(0:Object)}: Set) :=
   ⟨((n:ℕ):Object), by
     simp [Object.ofnat_eq',h]
@@ -155,7 +157,7 @@ theorem SetTheory.Set.f_3_3_3c_eval''' (n:ℕ) :
 /--
   Example 3.3.4 is a little tricky to replicate with the current formalism as the real numbers
   have not been constructed yet.  Instead, I offer some Mathlib counterparts, using the
-  Mathlib API for `NNReal` and `ℝ`.
+  Mathlib API for {name}`NNReal` and {lean}`ℝ`.
 -/
 example : ¬ ∃ f: ℝ → ℝ, ∀ x y, y = f x ↔ y^2 = x := by
   by_contra h
@@ -178,7 +180,7 @@ example : ∃ f: NNReal → NNReal, ∀ x y, y = f x ↔ y^2 = x := by
   · rw [h, NNReal.sq_sqrt]
   · rw [←h, NNReal.sqrt_sq]
 
-/-- Example 3.3.5. The unused variable `_x` is underscored to avoid triggering a linter. -/
+/-- Example 3.3.5. The unused variable {lit}`_x` is underscored to avoid triggering a linter. -/
 abbrev SetTheory.Set.P_3_3_5 : Nat → Nat → Prop := fun _x y ↦ y = 7
 
 theorem SetTheory.Set.P_3_3_5_existsUnique (x: Nat) : ∃! y: Nat, P_3_3_5 x y := by
@@ -221,7 +223,7 @@ example : (fun x:ℝ ↦ (x:ℝ)) ≠ (fun x:ℝ ↦ |(x:ℝ)|) := by
 
 /-- Example 3.3.11 -/
 abbrev SetTheory.Set.f_3_3_11 (X:Set) : Function (∅:Set) X :=
-  Function.mk (fun _ _ ↦ True) (by intro ⟨ x,hx ⟩; simp at hx)
+  Function.mk (fun _ _ ↦ True) (by intro ⟨ x, hx ⟩; simp at hx)
 
 theorem SetTheory.Set.empty_function_unique {X: Set} (f g: Function (∅:Set) X) : f = g := by sorry
 
@@ -271,8 +273,8 @@ theorem Function.one_to_one_iff {X Y: Set} (f: Function X Y) :
   peel with x hx; tauto
 
 /--
-  Compatibility with Mathlib's `Function.Injective`.  You may wish to use the `unfold` tactic to
-  understand Mathlib concepts such as `Function.Injective`.
+  Compatibility with Mathlib's {name}`Function.Injective`.  You may wish to use the {tactic}`unfold` tactic to
+  understand Mathlib concepts such as {name}`Function.Injective`.
 -/
 theorem Function.one_to_one_iff' {X Y: Set} (f: Function X Y) :
     f.one_to_one ↔ Function.Injective f.to_fn := by
@@ -307,7 +309,7 @@ theorem SetTheory.Set.two_to_one {X Y: Set} {f: Function X Y} (h: ¬ f.one_to_on
 /-- Definition 3.3.20 (Onto functions) -/
 abbrev Function.onto {X Y: Set} (f: Function X Y) : Prop := ∀ y: Y, ∃ x: X, f x = y
 
-/-- Compatibility with Mathlib's Function.Surjective-/
+/-- Compatibility with Mathlib's {name}`Function.Surjective` -/
 theorem Function.onto_iff {X Y: Set} (f: Function X Y) : f.onto ↔ Function.Surjective f.to_fn := by rfl
 
 /-- Example 3.3.21 (using Mathlib) -/
@@ -325,7 +327,7 @@ example : Function.Surjective (fun (n:ℤ) ↦ ⟨ n^2, by use n ⟩ : ℤ → A
 /-- Definition 3.3.23 (Bijective functions) -/
 abbrev Function.bijective {X Y: Set} (f: Function X Y) : Prop := f.one_to_one ∧ f.onto
 
-/-- Compatibility with Mathlib's Function.Bijective-/
+/-- Compatibility with Mathlib's {name}`Function.Bijective` -/
 theorem Function.bijective_iff {X Y: Set} (f: Function X Y) :
     f.bijective ↔ Function.Bijective f.to_fn := by
   rw [Function.bijective, Function.Bijective, one_to_one_iff', onto_iff]
@@ -386,9 +388,9 @@ theorem Function.bijective_incorrect_def :
   push_neg; use 0, 1; simp [f]
 
 /--
-  We cannot use the notation `f⁻¹` for the inverse because in Mathlib's `Inv` class, the inverse
-  of `f` must be exactly of the same type of `f`, and `Function Y X` is a different type from
-  `Function X Y`.
+  We cannot use the notation {syntax term}`f⁻¹` for the inverse because in Mathlib's {name}`Inv` class, the inverse
+  of {name}`f` must be exactly of the same type of {name}`f`, and {lean}`Function Y X` is a different type from
+  {lean}`Function X Y`.
 -/
 abbrev Function.inverse {X Y: Set} (f: Function X Y) (h: f.bijective) :
     Function Y X :=
@@ -414,7 +416,7 @@ theorem Function.inverse_eq {X Y: Set} [Nonempty X] {f: Function X Y} (h: f.bije
 
 /--
   Exercise 3.3.1.  Although a proof operating directly on functions would be shorter,
-  the spirit of the exercise is to show these using the `Function.eq_iff` definition.
+  the spirit of the exercise is to show these using the {name}`Function.eq_iff` definition.
 -/
 theorem Function.refl {X Y:Set} (f: Function X Y) : f = f := by sorry
 
diff --git a/analysis/Analysis/Section_3_4.lean b/Analysis/Section_3_4.lean
similarity index 96%
rename from analysis/Analysis/Section_3_4.lean
rename to Analysis/Section_3_4.lean
index e8dfb7c7..5d16c811 100644
--- a/analysis/Analysis/Section_3_4.lean
+++ b/Analysis/Section_3_4.lean
@@ -14,7 +14,7 @@ Main constructions and results of this section:
 
 - Images and inverse images of (Mathlib) functions, within the framework of Section 3.1 set
   theory. (The Section 3.3 functions are now deprecated and will not be used further.)
-- Connection with Mathlib's image `f '' S` and preimage `f ⁻¹' S` notions.
+- Connection with Mathlib's image {syntax term}`f '' S` and preimage {syntax term}`f ⁻¹' S` notions.
 
 ## Tips from past users
 
@@ -30,7 +30,7 @@ export SetTheory (Set Object nat)
 
 variable [SetTheory]
 
-/-- Definition 3.4.1.  Interestingly, the definition does not require S to be a subset of X. -/
+/-- Definition 3.4.1.  Interestingly, the definition does not require {lean}`S` to be a subset of {lean}`X`. -/
 abbrev SetTheory.Set.image {X Y:Set} (f:X → Y) (S: Set) : Set :=
   X.replace (P := fun x y ↦ f x = y ∧ x.val ∈ S) (by simp_all)
 
@@ -44,7 +44,7 @@ theorem SetTheory.Set.image_eq_specify {X Y:Set} (f:X → Y) (S: Set) :
     image f S = Y.specify (fun y ↦ ∃ x:X, x.val ∈ S ∧ f x = y) := by sorry
 
 /--
-  Connection with Mathlib's notion of image.  Note the need to utilize the `Subtype.val` coercion
+  Connection with Mathlib's notion of image.  Note the need to utilize the {name}`Subtype.val` coercion
   to make everything type consistent.
 -/
 theorem SetTheory.Set.image_eq_image {X Y:Set} (f:X → Y) (S: Set):
@@ -75,7 +75,7 @@ theorem SetTheory.Set.mem_image_of_eval_counter :
 
 /--
   Definition 3.4.4 (inverse images).
-  Again, it is not required that U be a subset of Y.
+  Again, it is not required that {lean}`U` be a subset of {lean}`Y`.
 -/
 abbrev SetTheory.Set.preimage {X Y:Set} (f:X → Y) (U: Set) : Set := X.specify (P := fun x ↦ (f x).val ∈ U)
 
@@ -84,7 +84,7 @@ theorem SetTheory.Set.mem_preimage {X Y:Set} (f:X → Y) (U: Set) (x:X) :
     x.val ∈ preimage f U ↔ (f x).val ∈ U := by rw [specification_axiom']
 
 /--
-  A version of mem_preimage that does not require x to be of type X.
+  A version of {name}`mem_preimage` that does not require {lean}`x` to be of type {lean}`X`.
 -/
 theorem SetTheory.Set.mem_preimage' {X Y:Set} (f:X → Y) (U: Set) (x:Object) :
     x ∈ preimage f U ↔ ∃ x': X, x'.val = x ∧ (f x').val ∈ U := by
@@ -126,9 +126,9 @@ instance SetTheory.Set.inst_pow : Pow Set Set where
 @[coe]
 def SetTheory.Set.coe_of_fun {X Y:Set} (f: X → Y) : Object := function_to_object X Y f
 
-/-- This coercion has to be a `CoeOut` rather than a
-`Coe` because the input type `X → Y` contains
-parameters not present in the output type `Output` -/
+/-- This coercion has to be a {name}`CoeOut` rather than a
+{name}`Coe` because the input type {lean}`X → Y` contains
+parameters not present in the output type {name}`Object` -/
 instance SetTheory.Set.inst_coe_of_fun {X Y:Set} : CoeOut (X → Y) Object where
   coe := coe_of_fun
 
@@ -335,7 +335,7 @@ theorem SetTheory.Set.partial_functions {X Y:Set} :
 
 /--
   Exercise 3.4.8.  The point of this exercise is to prove it without using the
-  pairwise union operation `∪`.
+  pairwise union operation {kw (of := «term_∪_»)}`∪`.
 -/
 theorem SetTheory.Set.union_pair_exists (X Y:Set) : ∃ Z:Set, ∀ x, x ∈ Z ↔ (x ∈ X ∨ x ∈ Y) := by
   sorry
diff --git a/analysis/Analysis/Section_3_5.lean b/Analysis/Section_3_5.lean
similarity index 92%
rename from analysis/Analysis/Section_3_5.lean
rename to Analysis/Section_3_5.lean
index 2fdc272f..71fcaf16 100644
--- a/analysis/Analysis/Section_3_5.lean
+++ b/Analysis/Section_3_5.lean
@@ -17,7 +17,7 @@ Main constructions and results of this section:
 - Ordered pairs and n-tuples.
 - Cartesian products and n-fold products.
 - Finite choice.
-- Connections with Mathlib counterparts such as `Set.pi` and `Set.prod`.
+- Connections with Mathlib counterparts such as {name}`Set.pi` and {name}`Set.prod`.
 
 ## Tips from past users
 
@@ -35,8 +35,8 @@ variable [SetTheory]
 
 open SetTheory.Set
 
-/-- Definition 3.5.1 (Ordered pair).  One could also have used `Object × Object` to
-define `OrderedPair` here. -/
+/-- Definition 3.5.1 (Ordered pair).  One could also have used {lean}`Object × Object` to
+define {name}`OrderedPair` here. -/
 @[ext]
 structure OrderedPair where
   fst: Object
@@ -63,7 +63,7 @@ instance OrderedPair.inst_coeObject : Coe OrderedPair Object where
   coe := toObject
 
 /--
-  A technical operation, turning a object `x` and a set `Y` to a set `{x} × Y`, needed to define
+  A technical operation, turning a object $`x` and a set $`Y` to a set $`{x} × Y`, needed to define
   the full Cartesian product
 -/
 abbrev SetTheory.Set.slice (x:Object) (Y:Set) : Set :=
@@ -105,7 +105,7 @@ theorem SetTheory.Set.pair_eq_fst_snd {X Y:Set} (z:X ×ˢ Y) :
   obtain ⟨ x, hx: z.val = (⟨ x, snd z ⟩:OrderedPair)⟩ := (exists_comm.mp this).choose_spec
   simp_all [EmbeddingLike.apply_eq_iff_eq]
 
-/-- This equips an `OrderedPair` with proofs that `x ∈ X` and `y ∈ Y`. -/
+/-- This equips an {name}`OrderedPair` with proofs that $`x ∈ X` and $`y ∈ Y`. -/
 def SetTheory.Set.mk_cartesian {X Y:Set} (x:X) (y:Y) : X ×ˢ Y :=
   ⟨(⟨ x, y ⟩:OrderedPair), by simp⟩
 
@@ -129,9 +129,10 @@ theorem SetTheory.Set.mk_cartesian_fst_snd_eq {X Y: Set} (z: X ×ˢ Y) :
   rw [mk_cartesian, Subtype.mk.injEq, pair_eq_fst_snd]
 
 /--
-  Connections with the Mathlib set product, which consists of Lean pairs like `(x, y)`
-  equipped with a proof that `x` is in the left set, and `y` is in the right set.
-  Lean pairs like `(x, y)` are similar to our `OrderedPair`, but more general.
+  {given -show}`x : X, y : Y`
+  Connections with the Mathlib set product, which consists of Lean pairs like {lean}`(x, y)`
+  equipped with a proof that {name}`x` is in the left set, and {name}`y` is in the right set.
+  Lean pairs like {lean}`(x, y)` are similar to our {name}`OrderedPair`, but more general.
 -/
 noncomputable abbrev SetTheory.Set.prod_equiv_prod (X Y:Set) :
     ((X ×ˢ Y):_root_.Set Object) ≃ (X:_root_.Set Object) ×ˢ (Y:_root_.Set Object) where
@@ -150,7 +151,7 @@ example : ({1, 2}: Set) ×ˢ ({3, 4, 5}: Set) = ({
   ((mk_cartesian (2: Nat) (5: Nat)): Object)
 }: Set) := by ext; aesop
 
-/-- Example 3.5.5 / Exercise 3.6.5. There is a bijection between `X ×ˢ Y` and `Y ×ˢ X`. -/
+/-- Example 3.5.5 / Exercise 3.6.5. There is a bijection between {lean}`X ×ˢ Y` and {lean}`Y ×ˢ X`. -/
 noncomputable abbrev SetTheory.Set.prod_commutator (X Y:Set) : X ×ˢ Y ≃ Y ×ˢ X where
   toFun := sorry
   invFun := sorry
@@ -164,7 +165,7 @@ noncomputable abbrev SetTheory.Set.curry_equiv {X Y Z:Set} : (X → Y → Z) ≃
   left_inv _ := by ext; simp
   right_inv _ := by simp
 
-/-- Definition 3.5.6.  The indexing set `I` plays the role of `{ i : 1 ≤ i ≤ n }` in the text.
+/-- Definition 3.5.6.  The indexing set {name}`I` plays the role of $`{ i : 1 ≤ i ≤ n }` in the text.
     See Exercise 3.5.10 below for some connections betweeen this concept and the preceding notion
     of Cartesian product and ordered pair.  -/
 abbrev SetTheory.Set.tuple {I:Set} {X: I → Set} (x: ∀ i, X i) : Object :=
@@ -190,7 +191,7 @@ theorem SetTheory.Set.tuple_mem_iProd {I: Set} {X: I → Set} (x: ∀ i, X i) :
 theorem SetTheory.Set.tuple_inj {I:Set} {X: I → Set} (x y: ∀ i, X i) :
     tuple x = tuple y ↔ x = y := by sorry
 
-/-- Example 3.5.8. There is a bijection between `(X ×ˢ Y) ×ˢ Z` and `X ×ˢ (Y ×ˢ Z)`. -/
+/-- Example 3.5.8. There is a bijection between {lean}`(X ×ˢ Y) ×ˢ Z` and {lean}`X ×ˢ (Y ×ˢ Z)`. -/
 noncomputable abbrev SetTheory.Set.prod_associator (X Y Z:Set) : (X ×ˢ Y) ×ˢ Z ≃ X ×ˢ (Y ×ˢ Z) where
   toFun p := mk_cartesian (fst (fst p)) (mk_cartesian (snd (fst p)) (snd p))
   invFun p := mk_cartesian (mk_cartesian (fst p) (fst (snd p))) (snd (snd p))
@@ -239,7 +240,7 @@ noncomputable abbrev SetTheory.Set.iProd_equiv_prod_triple (X: ({0,1,2}:Set) →
   left_inv := sorry
   right_inv := sorry
 
-/-- Connections with Mathlib's `Set.pi` -/
+/-- Connections with Mathlib's {name}`Set.pi` -/
 noncomputable abbrev SetTheory.Set.iProd_equiv_pi (I:Set) (X: I → Set) :
     iProd X ≃ Set.pi .univ (fun i:I ↦ ((X i):_root_.Set Object)) where
   toFun t := ⟨fun i ↦ ((mem_iProd _).mp t.property).choose i, by simp⟩
@@ -258,7 +259,7 @@ into the field of higher order category theory, which we will not pursue here.
 -/
 
 /--
-  Here we set up some an analogue of Mathlib `Fin n` types within the Chapter 3 Set Theory,
+  Here we set up some an analogue of Mathlib {lean}`Fin n` types within the Chapter 3 Set Theory,
   with rudimentary API.
 -/
 abbrev SetTheory.Set.Fin (n:ℕ) : Set := nat.specify (fun m ↦ (m:ℕ) < n)
@@ -328,7 +329,7 @@ abbrev SetTheory.Set.Fin_embed (n N:ℕ) (h: n ≤ N) (i: Fin n) : Fin N := ⟨
   have := i.property; rw [mem_Fin] at *; grind
 ⟩
 
-/-- Connections with Mathlib's `Fin n` -/
+/-- Connections with Mathlib's {lean}`Fin n` -/
 noncomputable abbrev SetTheory.Set.Fin.Fin_equiv_Fin (n:ℕ) : Fin n ≃ _root_.Fin n where
   toFun m := _root_.Fin.mk m (toNat_lt m)
   invFun m := Fin_mk n m.val m.isLt
@@ -375,8 +376,8 @@ structure SetTheory.Set.Tuple (n:ℕ) where
 
 /--
   Custom extensionality lemma for Exercise 3.5.2.
-  Placing `@[ext]` on the structure would generate a lemma requiring proof of `t.x = t'.x`,
-  but these functions have different types when `t.X ≠ t'.X`. This lemma handles that part.
+  Placing {attr}`@[ext]` on the structure would generate a lemma requiring proof of {lit}`t.x = t'.x`,
+  but these functions have different types when {lean}`t.X ≠ t'.X`. This lemma handles that part.
 -/
 @[ext]
 lemma SetTheory.Set.Tuple.ext {n:ℕ} {t t':Tuple n}
@@ -398,7 +399,7 @@ noncomputable abbrev SetTheory.Set.iProd_equiv_tuples (n:ℕ) (X: Fin n → Set)
 
 /--
   Exercise 3.5.3. The spirit here is to avoid direct rewrites (which make all of these claims
-  trivial), and instead use `OrderedPair.eq` or `SetTheory.Set.tuple_inj`
+  trivial), and instead use {name}`OrderedPair.eq` or {name}`SetTheory.Set.tuple_inj`
 -/
 theorem OrderedPair.refl (p: OrderedPair) : p = p := by sorry
 
@@ -487,8 +488,8 @@ theorem SetTheory.Set.is_graph {X Y G:Set} (hG: G ⊆ X ×ˢ Y)
     ∃! f: X → Y, G = graph f := by sorry
 
 /--
-  Exercise 3.5.11. This trivially follows from `SetTheory.Set.powerset_axiom`, but the
-  exercise is to derive it from `SetTheory.Set.exists_powerset` instead.
+  Exercise 3.5.11. This trivially follows from {name}`SetTheory.Set.powerset_axiom`, but the
+  exercise is to derive it from {name}`SetTheory.Set.exists_powerset` instead.
 -/
 theorem SetTheory.Set.powerset_axiom' (X Y:Set) :
     ∃! S:Set, ∀(F:Object), F ∈ S ↔ ∃ f: Y → X, f = F := sorry
diff --git a/analysis/Analysis/Section_3_6.lean b/Analysis/Section_3_6.lean
similarity index 93%
rename from analysis/Analysis/Section_3_6.lean
rename to Analysis/Section_3_6.lean
index 7cd1f2b5..d53d28db 100644
--- a/analysis/Analysis/Section_3_6.lean
+++ b/Analysis/Section_3_6.lean
@@ -208,7 +208,7 @@ theorem SetTheory.Set.nat_infinite : infinite nat := by
   apply_fun nat_equiv.symm at hi; simp_all
 
 open Classical in
-/-- It is convenient for Lean purposes to give infinite sets the ``junk`` cardinality of zero. -/
+/-- It is convenient for Lean purposes to give infinite sets the "junk" cardinality of zero. -/
 noncomputable def SetTheory.Set.card (X:Set) : ℕ := if h:X.finite then h.choose else 0
 
 theorem SetTheory.Set.has_card_card {X:Set} (hX: X.finite) : X.has_card (SetTheory.Set.card X) := by
@@ -311,14 +311,14 @@ lemma SetTheory.Set.pow_fun_eq_iff {A B : Set} (x y : ↑(A ^ B)) : x = y ↔ po
 theorem SetTheory.Set.card_pow {X Y:Set} (hY: Y.finite) (hX: X.finite) :
     (Y ^ X).finite ∧ (Y ^ X).card = Y.card ^ X.card := by sorry
 
-/-- Exercise 3.6.5. You might find `SetTheory.Set.prod_commutator` useful. -/
+/-- Exercise 3.6.5. You might find {name}`SetTheory.Set.prod_commutator` useful. -/
 theorem SetTheory.Set.prod_EqualCard_prod (A B:Set) :
     EqualCard (A ×ˢ B) (B ×ˢ A) := by sorry
 
 noncomputable abbrev SetTheory.Set.pow_fun_equiv' (A B : Set) : ↑(A ^ B) ≃ (B → A) :=
   pow_fun_equiv (A:=A) (B:=B)
 
-/-- Exercise 3.6.6. You may find `SetTheory.Set.curry_equiv` useful. -/
+/-- Exercise 3.6.6. You may find {name}`SetTheory.Set.curry_equiv` useful. -/
 theorem SetTheory.Set.pow_pow_EqualCard_pow_prod (A B C:Set) :
     EqualCard ((A ^ B) ^ C) (A ^ (B ×ˢ C)) := by sorry
 
@@ -369,7 +369,7 @@ theorem SetTheory.Set.Permutations_bijective {n: ℕ} (p: Permutations n) :
 theorem SetTheory.Set.Permutations_inj {n: ℕ} (p1 p2: Permutations n) :
     Permutations_toFun p1 = Permutations_toFun p2 ↔ p1 = p2 := by sorry
 
-/-- This connects our concept of a permutation with Mathlib's `Equiv` between `Fin n` and `Fin n`. -/
+/-- This connects our concept of a permutation with Mathlib's {name}`Equiv` between {lean}`Fin n` and {lean}`Fin n`. -/
 noncomputable def SetTheory.Set.perm_equiv_equiv {n : ℕ} : Permutations n ≃ (Fin n ≃ Fin n) := {
   toFun := fun p => Equiv.ofBijective (Permutations_toFun p) (Permutations_bijective p)
   invFun := sorry
@@ -379,7 +379,7 @@ noncomputable def SetTheory.Set.perm_equiv_equiv {n : ℕ} : Permutations n ≃
 
 /- Exercise 3.6.12 involves a lot of moving between `Fin n` and `Fin (n + 1)` so let's add some conveniences. -/
 
-/-- Any `Fin n` can be cast to `Fin (n + 1)`. Compare to Mathlib `Fin.castSucc`. -/
+/-- Any {lean}`Fin n` can be cast to {lean}`Fin (n + 1)`. Compare to Mathlib {name}`Fin.castSucc`. -/
 def SetTheory.Set.Fin.castSucc {n} (x : Fin n) : Fin (n + 1) :=
   Fin_embed _ _ (by omega) x
 
@@ -389,7 +389,7 @@ lemma SetTheory.Set.Fin.castSucc_inj {n} {x y : Fin n} : castSucc x = castSucc y
 @[simp]
 theorem SetTheory.Set.Fin.castSucc_ne {n} (x : Fin n) : castSucc x ≠ n := by sorry
 
-/-- Any `Fin (n + 1)` except `n` can be cast to `Fin n`. Compare to Mathlib `Fin.castPred`. -/
+/-- Any {lean}`Fin (n + 1)` except {lean}`n` can be cast to {lean}`Fin n`. Compare to Mathlib {name}`Fin.castPred`. -/
 noncomputable def SetTheory.Set.Fin.castPred {n} (x : Fin (n + 1)) (h : (x : ℕ) ≠ n) : Fin n :=
   Fin_mk _ (x : ℕ) (by have := Fin.toNat_lt x; omega)
 
@@ -401,7 +401,7 @@ theorem SetTheory.Set.Fin.castSucc_castPred {n} (x : Fin (n + 1)) (h : (x : ℕ)
 theorem SetTheory.Set.Fin.castPred_castSucc {n} (x : Fin n) (h : ((castSucc x : Fin (n + 1)) : ℕ) ≠ n) :
     castPred (castSucc x) h = x := by sorry
 
-/-- Any natural `n` can be cast to `Fin (n + 1)`. Compare to Mathlib `Fin.last`. -/
+/-- Any natural {lean}`n` can be cast to {lean}`Fin (n + 1)`. Compare to Mathlib {name}`Fin.last`. -/
 def SetTheory.Set.Fin.last (n : ℕ) : Fin (n + 1) := Fin_mk _ n (by omega)
 
 /-- Now is a good time to prove this result, which will be useful for completing Exercise 3.6.12 (i). -/
@@ -413,8 +413,8 @@ theorem SetTheory.Set.card_iUnion_card_disjoint {n m: ℕ} {S : Fin n → Set}
 /- Finally, we'll set up a way to shrink `Fin (n + 1)` into `Fin n` (or expand the latter) by making a hole. -/
 
 /--
-  If some `x : Fin (n+1)` is never equal to `i`, we can shrink it into `Fin n` by shifting all `x > i` down by one.
-  Compare to Mathlib `Fin.predAbove`.
+  If some {lean}`x : Fin (n+1)` is never equal to {name}`i`, we can shrink it into {lean}`Fin n` by shifting all {lean}`(x : ℕ) > i` down by one.
+  Compare to Mathlib {name}`Fin.predAbove`.
 -/
 noncomputable def SetTheory.Set.Fin.predAbove {n} (i : Fin (n + 1)) (x : Fin (n + 1)) (h : x ≠ i) : Fin n :=
   if hx : (x:ℕ) < i then
@@ -423,9 +423,9 @@ noncomputable def SetTheory.Set.Fin.predAbove {n} (i : Fin (n + 1)) (x : Fin (n
     Fin_mk _ ((x:ℕ) - 1) (by sorry)
 
 /--
-  We can expand `x : Fin n` into `Fin (n + 1)` by shifting all `x ≥ i` up by one.
-  The output is never `i`, so it forms an inverse to the shrinking done by `predAbove`.
-  Compare to Mathlib `Fin.succAbove`.
+  We can expand {lean}`x : Fin n` into {lean}`Fin (n + 1)` by shifting all {lean}`(x : ℕ) ≥ i` up by one.
+  The output is never {name}`i`, so it forms an inverse to the shrinking done by {name}`predAbove`.
+  Compare to Mathlib {name}`Fin.succAbove`.
 -/
 noncomputable def SetTheory.Set.Fin.succAbove {n} (i : Fin (n + 1)) (x : Fin n) : Fin (n + 1) :=
   if (x:ℕ) < i then
@@ -462,7 +462,7 @@ theorem SetTheory.Set.Permutations_ih (n: ℕ):
 theorem SetTheory.Set.Permutations_card (n: ℕ):
     (Permutations n).card = n.factorial := by sorry
 
-/-- Connections with Mathlib's `Finite` -/
+/-- Connections with Mathlib's {name}`Finite` -/
 theorem SetTheory.Set.finite_iff_finite {X:Set} : X.finite ↔ Finite X := by
   rw [finite_iff_exists_equiv_fin, finite]
   constructor
@@ -476,13 +476,13 @@ theorem SetTheory.Set.finite_iff_finite {X:Set} : X.finite ↔ Finite X := by
   have eq := hn.some.trans (Fin.Fin_equiv_Fin n).symm
   exact ⟨eq, eq.bijective⟩
 
-/-- Connections with Mathlib's `Set.Finite` -/
+/-- Connections with Mathlib's {name}`Set.Finite` -/
 theorem SetTheory.Set.finite_iff_set_finite {X:Set} :
     X.finite ↔ (X :_root_.Set Object).Finite := by
   rw [finite_iff_finite]
   rfl
 
-/-- Connections with Mathlib's `Nat.card` -/
+/-- Connections with Mathlib's {name}`Nat.card` -/
 theorem SetTheory.Set.card_eq_nat_card {X:Set} : X.card = Nat.card X := by
   by_cases hf : X.finite
   · by_cases hz : X.card = 0
@@ -500,7 +500,7 @@ theorem SetTheory.Set.card_eq_nat_card {X:Set} : X.card = Nat.card X := by
   right
   rwa [finite_iff_set_finite] at hf
 
-/-- Connections with Mathlib's `Set.ncard` -/
+/-- Connections with Mathlib's {name}`Set.ncard` -/
 theorem SetTheory.Set.card_eq_ncard {X:Set} : X.card = (X: _root_.Set Object).ncard := by
   rw [card_eq_nat_card]
   rfl
diff --git a/analysis/Analysis/Section_3_epilogue.lean b/Analysis/Section_3_epilogue.lean
similarity index 86%
rename from analysis/Analysis/Section_3_epilogue.lean
rename to Analysis/Section_3_epilogue.lean
index 9e63fb82..00c789f8 100644
--- a/analysis/Analysis/Section_3_epilogue.lean
+++ b/Analysis/Section_3_epilogue.lean
@@ -4,11 +4,13 @@ import Mathlib.SetTheory.ZFC.Basic
 import Analysis.Tools.ExistsUnique
 import Analysis.Section_3_1
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Chapter 3 epilogue: Connections with ZFSet
 
-In this epilogue we show that the `ZFSet` type in Mathlib (derived as a quotient from the
-`PSet` type) can be used to create models of the `SetTheory' class studied in this chapter, so long as we work in a universe of level at
+In this epilogue we show that the {name}`ZFSet` type in Mathlib (derived as a quotient from the
+{name}`PSet` type) can be used to create models of the `SetTheory` class studied in this chapter, so long as we work in a universe of level at
 least 1.  The constructions here are due to Edward van de Meent; see
 https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Can.20this.20proof.20related.20to.20Set.20replacement.20be.20shorter.3F/near/527305173
 -/
@@ -28,7 +30,7 @@ lemma PSet.mem_ofNat_iff (n m : ℕ) : ofNat n ∈ ofNat m ↔ n < m := by
   · exact mem_asymm (ofNat_mem_ofNat_of_lt _ _ h)
   apply mem_irrefl
 
-/-- Another preliminary lemma: Natural numbers in `PSet` can only be equivalent
+/-- Another preliminary lemma: Natural numbers in {name}`PSet` can only be equivalent
 if they are equal. -/
 lemma PSet.eq_of_ofNat_equiv_ofNat (n m : ℕ): (ofNat.{u} n).Equiv (ofNat.{u} m) → n = m := by
   wlog hmn : m ≤ n generalizing n m
@@ -38,7 +40,7 @@ lemma PSet.eq_of_ofNat_equiv_ofNat (n m : ℕ): (ofNat.{u} n).Equiv (ofNat.{u} m
   order
 
 open PSet in
-/-- Using the above lemmas, we can create a bijection between `ZFSet.omega` and
+/-- Using the above lemmas, we can create a bijection between {name}`ZFSet.omega` and
 the natural numbers. -/
 noncomputable def ZFSet.nat_equiv : ℕ ≃ omega.{u} := Equiv.ofBijective (fun n => ⟨mk (ofNat.{u} n),mk_mem_iff.mpr (Mem.mk _ (ULift.up n))⟩) (by
   constructor
@@ -48,9 +50,9 @@ noncomputable def ZFSet.nat_equiv : ℕ ≃ omega.{u} := Equiv.ofBijective (fun
   )
 
 open Classical in
-/-- Show that ZFSet obeys the `Chapter3.SetTheory` axioms.  Most of these axioms were
+/-- Show that {name}`ZFSet` obeys the {name}`Chapter3.SetTheory` axioms.  Most of these axioms were
 essentially already established in Mathlib and are relatively routine to transfer over;
-the equivalence of `ZF.omega` and `Nat` being the trickiest one in content (and the
+the equivalence of `ZF.omega` and {name}`Nat` being the trickiest one in content (and the
 power set axiom also requiring some technical manipulation). -/
 noncomputable instance ZFSet.inst_SetTheory : Chapter3.SetTheory.{u + 1,u + 1} where
   Set := ZFSet
diff --git a/analysis/Analysis/Section_4_1.lean b/Analysis/Section_4_1.lean
similarity index 98%
rename from analysis/Analysis/Section_4_1.lean
rename to Analysis/Section_4_1.lean
index a3b29d33..73776c8d 100644
--- a/analysis/Analysis/Section_4_1.lean
+++ b/Analysis/Section_4_1.lean
@@ -1,6 +1,8 @@
 import Mathlib.Tactic
 import Mathlib.Algebra.Group.MinimalAxioms
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 4.1: The integers
 
@@ -16,9 +18,9 @@ Main constructions and results of this section:
   natural numbers `a b:ℕ`, up to equivalence.  (This is a quotient of a scaffolding type
   `Section_4_1.PreInt`, which consists of formal differences without any equivalence imposed.)
 
-- ring operations and order these integers, as well as an embedding of ℕ.
+- ring operations and order these integers, as well as an embedding of {lean}`ℕ`.
 
-- Equivalence with the Mathlib integers `_root_.Int` (or `ℤ`), which we will use going forward.
+- Equivalence with the Mathlib integers {name}`_root_.Int` (or {lean}`ℤ`), which we will use going forward.
 
 ## Tips from past users
 
@@ -310,7 +312,7 @@ theorem Int.sq_nonneg (n:Int) : 0 ≤ n*n := by sorry
 theorem Int.sq_nonneg' (n:Int) : ∃ (m:Nat), n*n = m := by sorry
 
 /--
-  Not in textbook: create an equivalence between Int and ℤ.
+  Not in textbook: create an equivalence between {name}`Int` and {lean}`ℤ`.
   This requires some familiarity with the API for Mathlib's version of the integers.
 -/
 abbrev Int.equivInt : Int ≃ ℤ where
diff --git a/analysis/Analysis/Section_4_2.lean b/Analysis/Section_4_2.lean
similarity index 97%
rename from analysis/Analysis/Section_4_2.lean
rename to Analysis/Section_4_2.lean
index 138a6751..14f57bb5 100644
--- a/analysis/Analysis/Section_4_2.lean
+++ b/Analysis/Section_4_2.lean
@@ -1,6 +1,8 @@
 import Mathlib.Tactic
 import Mathlib.Algebra.Group.MinimalAxioms
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 4.2
 
@@ -19,11 +21,11 @@ Main constructions and results of this section:
   integers `a b:ℤ`, up to equivalence.  (This is a quotient of a scaffolding type
   `Section_4_2.PreRat`, which consists of formal quotients without any equivalence imposed.)
 
-- Field operations and order on these rationals, as well as an embedding of ℕ and ℤ.
+- Field operations and order on these rationals, as well as an embedding of {lean}`ℕ` and {lean}`ℤ`.
 
-- Equivalence with the Mathlib rationals `_root_.Rat` (or `ℚ`), which we will use going forward.
+- Equivalence with the Mathlib rationals {name}`_root_.Rat` (or {lean}`ℚ`), which we will use going forward.
 
-Note: here (and in the sequel) we use Mathlib's natural numbers `ℕ` and integers `ℤ` rather than
+Note: here (and in the sequel) we use Mathlib's natural numbers {lean}`ℕ` and integers {lean}`ℤ` rather than
 the Chapter 2 natural numbers and Section 4.1 integers.
 
 ## Tips from past users
@@ -73,9 +75,10 @@ theorem Rat.eq_diff (n:Rat) : ∃ a b, b ≠ 0 ∧ n = a // b := by
   simp [formalDiv, h]
 
 /--
-  Decidability of equality. Hint: modify the proof of `DecidableEq Int` from the previous
+  Decidability of equality. Hint: modify the proof of {lean}`DecidableEq Int` from the previous
   section. However, because formal division handles the case of zero denominator separately, it
-  may be more convenient to avoid that operation and work directly with the `Quotient` API.
+  may be more convenient to avoid that operation and work directly with the {name}`Quotient` API.
+
 -/
 instance Rat.decidableEq : DecidableEq Rat := by
   sorry
diff --git a/analysis/Analysis/Section_4_3.lean b/Analysis/Section_4_3.lean
similarity index 99%
rename from analysis/Analysis/Section_4_3.lean
rename to Analysis/Section_4_3.lean
index f96634e7..094799a1 100644
--- a/analysis/Analysis/Section_4_3.lean
+++ b/Analysis/Section_4_3.lean
@@ -12,7 +12,7 @@ doing so.
 Main constructions and results of this section:
 
 - Basic properties of absolute value and exponentiation on the rational numbers (here we use the
-  Mathlib rational numbers `ℚ` rather than the Section 4.2 rational numbers).
+  Mathlib rational numbers {lean}`ℚ` rather than the Section 4.2 rational numbers).
 
 Note: to avoid notational conflict, we are using the standard Mathlib definitions of absolute
 value and exponentiation.  As such, it is possible to solve several of the exercises here rather
diff --git a/analysis/Analysis/Section_4_4.lean b/Analysis/Section_4_4.lean
similarity index 100%
rename from analysis/Analysis/Section_4_4.lean
rename to Analysis/Section_4_4.lean
diff --git a/analysis/Analysis/Section_5_1.lean b/Analysis/Section_5_1.lean
similarity index 88%
rename from analysis/Analysis/Section_5_1.lean
rename to Analysis/Section_5_1.lean
index 96b33dbf..7e37fd91 100644
--- a/analysis/Analysis/Section_5_1.lean
+++ b/Analysis/Section_5_1.lean
@@ -1,6 +1,8 @@
 import Mathlib.Tactic
 import Analysis.Section_4_3
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 5.1: Cauchy sequences
 
@@ -27,7 +29,7 @@ namespace Chapter5
 
 /--
   Definition 5.1.1 (Sequence). To avoid some technicalities involving dependent types, we extend
-  sequences by zero to the left of the starting point `n₀`.
+  sequences by zero to the left of the starting point {name (full := Sequence.n₀)}`n₀`.
 -/
 @[ext]
 structure Sequence where
@@ -35,26 +37,26 @@ structure Sequence where
   seq : ℤ → ℚ
   vanish : ∀ n < n₀, seq n = 0
 
-/-- Sequences can be thought of as functions from ℤ to ℚ. -/
+/-- Sequences can be thought of as functions from {lean}`ℤ` to {lean}`ℚ`. -/
 instance Sequence.instCoeFun : CoeFun Sequence (fun _ ↦ ℤ → ℚ) where
   coe := fun a ↦ a.seq
 
 /--
-Functions from ℕ to ℚ can be thought of as sequences starting from 0; `ofNatFun` performs this conversion.
+Functions from {lean}`ℕ` to {lean}`ℚ` can be thought of as sequences starting from 0; {name}`Sequence.ofNatFun` performs this conversion.
 
-The `coe` attribute allows the delaborator to print `Sequence.ofNatFun f` as `↑f`, which is more concise; you may safely remove this if you prefer the more explicit notation.
+The {attr}`coe` attribute allows the delaborator to print {lean}`Sequence.ofNatFun f` as {lit}`↑f`, which is more concise; you may safely remove this if you prefer the more explicit notation.
 -/
 @[coe]
-def Sequence.ofNatFun (a : ℕ → ℚ) : Sequence where
+def Sequence.ofNatFun (f : ℕ → ℚ) : Sequence where
     n₀ := 0
-    seq n := if n ≥ 0 then a n.toNat else 0
+    seq n := if n ≥ 0 then f n.toNat else 0
     vanish := by grind
 
 -- Notice how the delaborator prints this as `↑fun x ↦ ↑x ^ 2 : Sequence`.
 #check Sequence.ofNatFun (· ^ 2)
 
 /--
-If `a : ℕ → ℚ` is used in a context where a `Sequence` is expected, automatically coerce `a` to `Sequence.ofNatFun a` (which will be pretty-printed as `↑a`)
+If {given}`a : ℕ → ℚ` is used in a context where a {name}`Sequence` is expected, automatically coerce {name}`a` to {lean}`Sequence.ofNatFun a` (which will be pretty-printed as {lean (type :="Sequence")}`↑a`).
 -/
 instance : Coe (ℕ → ℚ) Sequence where
   coe := Sequence.ofNatFun
@@ -99,8 +101,8 @@ example (n:ℤ) (hn: n ≥ 3) : Sequence.squares_from_three n = n^2 := Sequence.
 end Chapter5
 
 /--
-A slight generalization of Definition 5.1.3 - definition of ε-steadiness for a sequence with an
-arbitrary starting point n₀
+A slight generalization of Definition 5.1.3 - definition of {name}`ε`-steadiness for a sequence with an
+arbitrary starting point {lean}`a.n₀`
 -/
 abbrev Rat.Steady (ε: ℚ) (a: Chapter5.Sequence) : Prop :=
   ∀ n ≥ a.n₀, ∀ m ≥ a.n₀, ε.Close (a n) (a m)
@@ -111,7 +113,7 @@ lemma Rat.steady_def (ε: ℚ) (a: Chapter5.Sequence) :
 namespace Chapter5
 
 /--
-Definition 5.1.3 - definition of ε-steadiness for a sequence starting at 0
+Definition 5.1.3 - definition of {name}`ε`-steadiness for a sequence starting at 0
 -/
 lemma Rat.Steady.coe (ε : ℚ) (a:ℕ → ℚ) :
     ε.Steady a ↔ ∀ n m : ℕ, ε.Close (a n) (a m) := by
@@ -123,15 +125,16 @@ lemma Rat.Steady.coe (ε : ℚ) (a:ℕ → ℚ) :
   simp [h n m]
 
 /--
-Not in textbook: the sequence 3, 3 ... is 1-steady
-Intended as a demonstration of `Rat.Steady.coe`
+Not in textbook: the sequence 3, 3 ... is 1-steady.
+Intended as a demonstration of {name}`Rat.Steady.coe`.
 -/
 example : (1:ℚ).Steady ((fun _:ℕ ↦ (3:ℚ)):Sequence) := by
   simp [Rat.Steady.coe, Rat.Close]
 
 /--
-Compare: if you need to work with `Rat.Steady` on the coercion directly, there will be side
-conditions `hn : n ≥ 0` and `hm : m ≥ 0` that you will need to deal with.
+{given -show}`hn : n ≥ 0, hm : m ≥ 0`
+Compare: if you need to work with {name}`Rat.Steady` on the coercion directly, there will be side
+conditions {lean}`hn : n ≥ 0` and {lean}`hm : m ≥ 0` that you will need to deal with.
 -/
 example : (1:ℚ).Steady ((fun _:ℕ ↦ (3:ℚ)):Sequence) := by
   intro n _ m _; simp_all [Sequence.n0_coe, Sequence.eval_coe_at_int, Rat.Close]
@@ -197,8 +200,8 @@ example (ε:ℚ) (hε:ε<10):  ¬ ε.Steady ((fun n:ℕ ↦ if n = 0 then (10:
   contrapose! hε; rw [Rat.Steady.coe] at hε; specialize hε 0 1; simpa [Rat.Close] using hε
 
 /--
-  a.from n₁ starts `a:Sequence` from `n₁`.  It is intended for use when `n₁ ≥ n₀`, but returns
-  the "junk" value of the original sequence `a` otherwise.
+  {name}`Sequence.from` starts {lean}`a : Sequence` from {name}`n₁`.  It is intended for use when {lean}`n₁ ≥ n₀`, but returns
+  the "junk" value of the original sequence {name}`a` otherwise.
 -/
 abbrev Sequence.from (a:Sequence) (n₁:ℤ) : Sequence :=
   mk' (max a.n₀ n₁) (fun n ↦ a (n:ℤ))
@@ -223,7 +226,7 @@ lemma Sequence.ex_5_1_7_a : ¬ (0.1:ℚ).Steady ((fun n:ℕ ↦ (n+1:ℚ)⁻¹ )
   intro h; rw [Rat.Steady.coe] at h; specialize h 0 2; simp [Rat.Close] at h; norm_num at h
 
 /--
-Example 5.1.7: The sequence a_10, a_11, a_12, ... is 0.1-steady
+Example 5.1.7: The sequence `a_10, a_11, a_12, ...` is 0.1-steady
 -/
 lemma Sequence.ex_5_1_7_b : (0.1:ℚ).Steady (((fun n:ℕ ↦ (n+1:ℚ)⁻¹ ):Sequence).from 10) := by
   rw [Rat.Steady]
@@ -260,7 +263,7 @@ abbrev Sequence.IsCauchy (a:Sequence) : Prop := ∀ ε > (0:ℚ), ε.EventuallyS
 lemma Sequence.isCauchy_def (a:Sequence) :
   a.IsCauchy ↔ ∀ ε > (0:ℚ), ε.EventuallySteady a := by rfl
 
-/-- Definition of Cauchy sequences, for a sequence starting at 0 -/
+/-- Definition of Cauchy sequences, for a sequence starting at {lean}`0` -/
 lemma Sequence.IsCauchy.coe (a:ℕ → ℚ) :
     (a:Sequence).IsCauchy ↔ ∀ ε > (0:ℚ), ∃ N, ∀ j ≥ N, ∀ k ≥ N,
     Section_4_3.dist (a j) (a k) ≤ ε := by
@@ -344,7 +347,7 @@ theorem Sequence.IsCauchy.harmonic : (mk' 1 (fun n ↦ (1:ℚ)/n)).IsCauchy := b
 abbrev BoundedBy {n:ℕ} (a: Fin n → ℚ) (M:ℚ) : Prop := ∀ i, |a i| ≤ M
 
 /--
-  Definition 5.1.12 (bounded sequences). Here we start sequences from 0 rather than 1 to align
+  Definition 5.1.12 (bounded sequences). Here we start sequences from {lean}`0` rather than {lean}`1` to align
   better with Mathlib conventions.
 -/
 lemma boundedBy_def {n:ℕ} (a: Fin n → ℚ) (M:ℚ) : BoundedBy a M ↔ ∀ i, |a i| ≤ M := by rfl
diff --git a/analysis/Analysis/Section_5_2.lean b/Analysis/Section_5_2.lean
similarity index 100%
rename from analysis/Analysis/Section_5_2.lean
rename to Analysis/Section_5_2.lean
diff --git a/analysis/Analysis/Section_5_3.lean b/Analysis/Section_5_3.lean
similarity index 95%
rename from analysis/Analysis/Section_5_3.lean
rename to Analysis/Section_5_3.lean
index 5a2a52fb..573a42ee 100644
--- a/analysis/Analysis/Section_5_3.lean
+++ b/Analysis/Section_5_3.lean
@@ -28,7 +28,7 @@ Users of the companion who have completed the exercises in this section are welc
 
 namespace Chapter5
 
-/-- A class of Cauchy sequences that start at zero -/
+/-- A class of Cauchy sequences that start at zero. -/
 @[ext]
 class CauchySequence extends Sequence where
   zero : n₀ = 0
@@ -38,7 +38,7 @@ theorem CauchySequence.ext' {a b: CauchySequence} (h: a.seq = b.seq) : a = b :=
   apply CauchySequence.ext _ h
   rw [a.zero, b.zero]
 
-/-- A sequence starting at zero that is Cauchy, can be viewed as a Cauchy sequence.-/
+/-- A sequence starting at zero that is Cauchy, can be viewed as a {name}`CauchySequence`. -/
 abbrev CauchySequence.mk' {a:ℕ → ℚ} (ha: (a:Sequence).IsCauchy) : CauchySequence where
   n₀ := 0
   seq := (a:Sequence).seq
@@ -78,7 +78,7 @@ instance CauchySequence.instSetoid : Setoid CauchySequence where
 
 theorem CauchySequence.equiv_iff (a b: CauchySequence) : a ≈ b ↔ Sequence.Equiv a b := by rfl
 
-/-- Every constant sequence is Cauchy -/
+/-- Every constant sequence is Cauchy. -/
 theorem Sequence.IsCauchy.const (a:ℚ) : ((fun _:ℕ ↦ a):Sequence).IsCauchy := by sorry
 
 instance CauchySequence.instZero : Zero CauchySequence where
@@ -88,8 +88,8 @@ abbrev Real := Quotient CauchySequence.instSetoid
 
 open Classical in
 /--
-  It is convenient in Lean to assign the "dummy" value of 0 to `LIM a` when `a` is not Cauchy.
-  This requires Classical logic, because the property of being Cauchy is not computable or
+  It is convenient in Lean to assign the "dummy" value of {lean}`0` to {lean}`LIM a` when {lean}`a` is not Cauchy.
+  This requires classical logic, because the property of being Cauchy is not computable or
   decidable.
 -/
 noncomputable abbrev LIM (a:ℕ → ℚ) : Real :=
@@ -238,19 +238,19 @@ theorem Real.LIM.zero : LIM (fun _ ↦ (0:ℚ)) = 0 := by rw [←ratCast_def 0];
 instance Real.instIntCast : IntCast Real where
   intCast n := ((n:ℚ):Real)
 
-/-- ratCast distributes over addition -/
+/-- {name (full := RatCast.ratCast)}`ratCast` distributes over addition -/
 theorem Real.ratCast_add (a b:ℚ) : (a:Real) + (b:Real) = (a+b:ℚ) := by sorry
 
-/-- ratCast distributes over multiplication -/
+/-- {name (full := RatCast.ratCast)}`ratCast` distributes over multiplication -/
 theorem Real.ratCast_mul (a b:ℚ) : (a:Real) * (b:Real) = (a*b:ℚ) := by sorry
 
 noncomputable instance Real.instNeg : Neg Real where
   neg x := ((-1:ℚ):Real) * x
 
-/-- ratCast commutes with negation -/
+/-- {name (full := RatCast.ratCast)}`ratCast` commutes with negation -/
 theorem Real.neg_ratCast (a:ℚ) : -(a:Real) = (-a:ℚ) := by sorry
 
-/-- It may be possible to omit the Cauchy sequence hypothesis here. -/
+/-- It may be possible to omit the {name (full := Sequence.IsCauchy)}`IsCauchy` hypothesis here. -/
 theorem Real.neg_LIM (a:ℕ → ℚ) (ha: (a:Sequence).IsCauchy) : -LIM a = LIM (-a) := by sorry
 
 theorem Sequence.IsCauchy.neg (a:ℕ → ℚ) (ha: (a:Sequence).IsCauchy) :
@@ -265,11 +265,11 @@ theorem Real.sub_eq_add_neg (x y:Real) : x - y = x + (-y) := rfl
 theorem Sequence.IsCauchy.sub {a b:ℕ → ℚ} (ha: (a:Sequence).IsCauchy) (hb: (b:Sequence).IsCauchy) :
     ((a-b:ℕ → ℚ):Sequence).IsCauchy := by sorry
 
-/-- LIM distributes over subtraction -/
+/-- {name}`LIM` distributes over subtraction -/
 theorem Real.LIM_sub {a b:ℕ → ℚ} (ha: (a:Sequence).IsCauchy) (hb: (b:Sequence).IsCauchy) :
   LIM a - LIM b = LIM (a - b) := by sorry
 
-/-- ratCast distributes over subtraction -/
+/-- {name (full := RatCast.ratCast)}`ratCast` distributes over subtraction -/
 theorem Real.ratCast_sub (a b:ℚ) : (a:Real) - (b:Real) = (a-b:ℚ) := by sorry
 
 /-- Proposition 5.3.11 (laws of algebra) -/
@@ -432,7 +432,7 @@ theorem Real.inv_ratCast (q:ℚ) : (q:Real)⁻¹ = (q⁻¹:ℚ) := by
   . rw [h, ← show (0:Real) = (0:ℚ) by norm_cast]; norm_num; norm_cast
   simp_rw [ratCast_def, inv_def (BoundedAwayZero.const h) (by apply Sequence.IsCauchy.const)]; congr
 
-/-- Default definition of division -/
+/-- Default definition of division. -/
 noncomputable instance Real.instDivInvMonoid : DivInvMonoid Real where
 
 theorem Real.div_eq (x y:Real) : x/y = x * y⁻¹ := rfl
@@ -455,7 +455,7 @@ theorem Real.IsBounded.equiv {a b:ℕ → ℚ} (ha: (a:Sequence).IsBounded) (hab
     (b:Sequence).IsBounded := by sorry
 
 /--
-  Same as `Sequence.IsCauchy.harmonic` but reindexing the sequence as a₀ = 1, a₁ = 1/2, ...
+  Same as {name}`Sequence.IsCauchy.harmonic` but reindexing the sequence as a₀ = 1, a₁ = 1/2, ...
   This form is more convenient for the upcoming proof of Theorem 5.5.9.
 -/
 theorem Sequence.IsCauchy.harmonic' : ((fun n ↦ 1/((n:ℚ)+1): ℕ → ℚ):Sequence).IsCauchy := by
diff --git a/analysis/Analysis/Section_5_4.lean b/Analysis/Section_5_4.lean
similarity index 97%
rename from analysis/Analysis/Section_5_4.lean
rename to Analysis/Section_5_4.lean
index 568460be..4cc185b0 100644
--- a/analysis/Analysis/Section_5_4.lean
+++ b/Analysis/Section_5_4.lean
@@ -117,7 +117,7 @@ theorem Real.pos_of_coe (q:ℚ) : (q:Real).IsPos ↔ q > 0 := by sorry
 theorem Real.neg_of_coe (q:ℚ) : (q:Real).IsNeg ↔ q < 0 := by sorry
 
 open Classical in
-/-- Need to use classical logic here because isPos and isNeg are not decidable -/
+/-- Need to use classical logic here because {name}`IsPos` and {name}`IsNeg` are not decidable -/
 noncomputable abbrev Real.abs (x:Real) : Real := if x.IsPos then x else (if x.IsNeg then -x else 0)
 
 /-- Definition 5.4.5 (absolute value) -/
@@ -192,7 +192,7 @@ theorem Real.mul_pos_neg {x y:Real} (hx: x.IsPos) (hy: y.IsNeg) : (x * y).IsNeg
 
 open Classical in
 /--
-  (Not from textbook) Real has the structure of a linear ordering. The order is not computable,
+  (Not from textbook) {name}`Real` has the structure of a linear ordering. The order is not computable,
   and so classical logic is required to impose decidability.
 -/
 noncomputable instance Real.instLinearOrder : LinearOrder Real where
@@ -204,7 +204,7 @@ noncomputable instance Real.instLinearOrder : LinearOrder Real where
   toDecidableLE := Classical.decRel _
 
 /--
-  (Not from textbook) Linear Orders come with a definition of absolute value |.|
+  (Not from textbook) {name}`LinearOrder`s come with a definition of absolute value {lean (type := "Real → Real")}`(|·|)`.
   Show that it agrees with our earlier definition.
 -/
 theorem Real.abs_eq_abs (x:Real) : |x| = abs x := by sorry
@@ -237,7 +237,7 @@ theorem Real.inv_of_gt {x y:Real} (hx: x.IsPos) (hy: y.IsPos) (hxy: x > y) : x
     _ = _ := self_mul_inv hynon
   simp at this
 
-/-- (Not from textbook) Real has the structure of a strict ordered ring. -/
+/-- (Not from textbook) {name}`Real` has the structure of a strict ordered ring. -/
 instance Real.instIsStrictOrderedRing : IsStrictOrderedRing Real where
   add_le_add_left := by sorry
   add_le_add_right := by sorry
diff --git a/analysis/Analysis/Section_5_5.lean b/Analysis/Section_5_5.lean
similarity index 96%
rename from analysis/Analysis/Section_5_5.lean
rename to Analysis/Section_5_5.lean
index e822ed98..b1a5e057 100644
--- a/analysis/Analysis/Section_5_5.lean
+++ b/Analysis/Section_5_5.lean
@@ -25,7 +25,7 @@ Users of the companion who have completed the exercises in this section are welc
 
 namespace Chapter5
 
-/-- Definition 5.5.1 (upper bounds).  Here we use the `upperBounds` set defined in Mathlib. -/
+/-- Definition 5.5.1 (upper bounds). Here we use the {name}`upperBounds` set defined in Mathlib. -/
 theorem Real.upperBound_def (E: Set Real) (M: Real) : M ∈ upperBounds E ↔ ∀ x ∈ E, x ≤ M :=
   mem_upperBounds
 
@@ -53,7 +53,7 @@ example : ∀ M, M ∈ upperBounds (∅ : Set Real) := by sorry
 theorem Real.upperBound_upper {M M': Real} (h: M ≤ M') {E: Set Real} (hb: M ∈ upperBounds E) :
     M' ∈ upperBounds E := by sorry
 
-/-- Definition 5.5.5 (least upper bound).  Here we use the `isLUB` predicate defined in Mathlib. -/
+/-- Definition 5.5.5 (least upper bound).  Here we use the {name}`IsLUB` predicate defined in Mathlib. -/
 theorem Real.isLUB_def (E: Set Real) (M: Real) :
     IsLUB E M ↔ M ∈ upperBounds E ∧ ∀ M' ∈ upperBounds E, M' ≥ M := by rfl
 
@@ -70,7 +70,7 @@ example : ¬∃ M, IsLUB (∅: Set Real) M := by sorry
 theorem Real.LUB_unique {E: Set Real} {M M': Real} (h1: IsLUB E M) (h2: IsLUB E M') : M = M' := by
   grind [Real.isLUB_def]
 
-/-- definition of "bounded above", using Mathlib notation -/
+/-- Definition of "bounded above", using Mathlib notation -/
 theorem Real.bddAbove_def (E: Set Real) : BddAbove E ↔ ∃ M, M ∈ upperBounds E := Set.nonempty_def
 
 theorem Real.bddBelow_def (E: Set Real) : BddBelow E ↔ ∃ M, M ∈ lowerBounds E := Set.nonempty_def
@@ -194,11 +194,11 @@ inductive ExtendedReal where
 | real (x:Real) : ExtendedReal
 | infty : ExtendedReal
 
-/-- Mathlib prefers ⊤ to denote the +∞ element. -/
+/-- Mathlib prefers {syntax term}`⊤` to denote the +∞ element. -/
 instance ExtendedReal.inst_Top : Top ExtendedReal where
   top := infty
 
-/-- Mathlib prefers ⊥ to denote the -∞ element.-/
+/-- Mathlib prefers {syntax term}`⊥` to denote the -∞ element. -/
 instance ExtendedReal.inst_Bot: Bot ExtendedReal where
   bot := neg_infty
 
@@ -334,7 +334,7 @@ theorem Real.irrat_between {x y:Real} (hxy: x < y) :
 noncomputable instance Real.inst_SupSet : SupSet Real where
   sSup E := ((ExtendedReal.sup E):Real)
 
-/-- Use the `sSup` operation to build a conditionally complete lattice structure on `Real`-/
+/-- Use the {name}`sSup` operation to build a conditionally complete lattice structure on {name}`Real`. -/
 noncomputable instance Real.inst_conditionallyCompleteLattice :
     ConditionallyCompleteLattice Real :=
   conditionallyCompleteLatticeOfLatticeOfsSup Real
diff --git a/analysis/Analysis/Section_5_6.lean b/Analysis/Section_5_6.lean
similarity index 97%
rename from analysis/Analysis/Section_5_6.lean
rename to Analysis/Section_5_6.lean
index d1660803..7cafbac8 100644
--- a/analysis/Analysis/Section_5_6.lean
+++ b/Analysis/Section_5_6.lean
@@ -28,7 +28,7 @@ Users of the companion who have completed the exercises in this section are welc
 namespace Chapter5
 
 /-- Definition 5.6.1 (Exponentiating a real by a natural number). Here we use the
-    Mathlib definition coming from `Monoid`. -/
+    Mathlib definition coming from {name}`Monoid`. -/
 
 lemma Real.pow_zero (x: Real) : x ^ 0 = 1 := rfl
 
@@ -67,7 +67,7 @@ theorem Real.pow_gt_pow (x y:Real) (n:ℕ) (hxy: x > y) (hy: y ≥ 0) (hn: n > 0
 /-- Analogue of Proposition 4.3.10(d) -/
 theorem Real.pow_abs (x:Real) (n:ℕ) : |x|^n = |x^n| := by sorry
 
-/-- Definition 5.6.2 (Exponentiating a real by an integer). Here we use the Mathlib definition coming from `DivInvMonoid`. -/
+/-- Definition 5.6.2 (Exponentiating a real by an integer). Here we use the Mathlib definition coming from {name}`DivInvMonoid`. -/
 lemma Real.pow_eq_pow (x: Real) (n:ℕ): x ^ (n:ℤ) = x ^ n := by rfl
 
 @[simp]
@@ -100,7 +100,7 @@ theorem Real.zpow_inj {x y:Real} {n:ℤ} (hx: x > 0) (hy : y > 0) (hn: n ≠ 0)
 /-- Analogue of Proposition 4.3.12(d) -/
 theorem Real.zpow_abs (x:Real) (n:ℤ) : |x|^n = |x^n| := by sorry
 
-/-- Definition 5.6.2.  We permit ``junk values'' when `x` is negative or `n` vanishes. -/
+/-- Definition 5.6.2. We permit "junk values" when {lean}`x` is negative or {lean}`n` vanishes. -/
 noncomputable abbrev Real.root (x:Real) (n:ℕ) : Real := sSup { y:Real | y ≥ 0 ∧ y^n ≤ x }
 
 noncomputable abbrev Real.sqrt (x:Real) := x.root 2
diff --git a/analysis/Analysis/Section_5_epilogue.lean b/Analysis/Section_5_epilogue.lean
similarity index 88%
rename from analysis/Analysis/Section_5_epilogue.lean
rename to Analysis/Section_5_epilogue.lean
index eb09bb82..c1588d66 100644
--- a/analysis/Analysis/Section_5_epilogue.lean
+++ b/Analysis/Section_5_epilogue.lean
@@ -4,16 +4,16 @@ import Analysis.Section_5_6
 /-!
 # Analysis I, Chapter 5 epilogue: Isomorphism with the Mathlib real numbers
 
-In this (technical) epilogue, we show that the "Chapter 5" real numbers `Chapter5.Real` are
-isomorphic in various standard senses to the standard real numbers `ℝ`.  This we do by matching
-both structures with Dedekind cuts of the (Mathlib) rational numbers `ℚ`.
+In this (technical) epilogue, we show that the "Chapter 5" real numbers {name}`Chapter5.Real` are
+isomorphic in various standard senses to the standard real numbers {lean}`ℝ`.  This we do by matching
+both structures with Dedekind cuts of the (Mathlib) rational numbers {lean}`ℚ`.
 
-From this point onwards, `Chapter5.Real` will be deprecated, and we will use the standard real
-numbers `ℝ` instead.  In particular, one should use the full Mathlib API for `ℝ` for all
-subsequent chapters, in lieu of the `Chapter5.Real` API.
+From this point onwards, {name}`Chapter5.Real` will be deprecated, and we will use the standard real
+numbers {lean}`ℝ` instead.  In particular, one should use the full Mathlib API for {lean}`ℝ` for all
+subsequent chapters, in lieu of the {name}`Chapter5.Real` API.
 
-Filling the sorries here requires both the Chapter5.Real API and the Mathlib API for the standard
-natural numbers `ℝ`.  As such, they are excellent exercises to prepare you for the aforementioned
+Filling the {syntax term}`sorry`s here requires both the {name}`Chapter5.Real` API and the Mathlib API for the standard
+real numbers {lean}`ℝ`.  As such, they are excellent exercises to prepare you for the aforementioned
 transition.
 
 ## Tips from past users
@@ -124,7 +124,7 @@ noncomputable abbrev Real.equivCut : ℝ ≃ Chapter5.DedekindCut where
 
 namespace Chapter5
 
-/-- The isomorphism between the Chapter 5 reals and the Mathlib reals. -/
+/-- The isomorphism between the {name}`Chapter5.Real` numbers and the Mathlib reals. -/
 noncomputable abbrev Real.equivR : Real ≃ ℝ := Real.equivCut.trans _root_.Real.equivCut.symm
 
 lemma Real.equivR_iff (x : Real) (y : ℝ) : y = Real.equivR x ↔ y.toCut = x.toCut := by
@@ -151,14 +151,14 @@ theorem Sequence.IsCauchy.to_IsCauSeq {a: ℕ → ℚ} (ha: IsCauchy a) : IsCauS
   sorry
 
 -- Convertion of an `IsCauchy` to a `CauSeq`
-abbrev Sequence.IsCauchy.CauSeq {a: ℕ → ℚ} : (ha: IsCauchy a) → CauSeq ℚ _root_.abs := 
+abbrev Sequence.IsCauchy.CauSeq {a: ℕ → ℚ} : (ha: IsCauchy a) → CauSeq ℚ _root_.abs :=
   (⟨a, ·.to_IsCauSeq⟩)
 
--- We then set up the conversion from Sequence.Equiv to CauSeq.LimZero because 
+-- We then set up the conversion from Sequence.Equiv to CauSeq.LimZero because
 -- it is the equivalence relation
 example {a b: CauSeq ℚ abs} : a ≈ b ↔ CauSeq.LimZero (a - b) := by rfl
 
-theorem Sequence.Equiv.LimZero {a b: ℕ → ℚ} (ha: IsCauchy a) (hb: IsCauchy b) (h:Equiv a b) 
+theorem Sequence.Equiv.LimZero {a b: ℕ → ℚ} (ha: IsCauchy a) (hb: IsCauchy b) (h:Equiv a b)
   : CauSeq.LimZero (ha.CauSeq - hb.CauSeq) := by
     sorry
 
@@ -167,7 +167,7 @@ theorem Real.mk_eq_mk {a b: ℕ → ℚ} (ha : Sequence.IsCauchy a) (hb : Sequen
   : Real.mk ha.CauSeq = Real.mk hb.CauSeq := Real.mk_eq.mpr (hab.LimZero ha hb)
 
 -- Both directions of the equivalence
-theorem Sequence.Equiv_iff_LimZero {a b: ℕ → ℚ} (ha: IsCauchy a) (hb: IsCauchy b) 
+theorem Sequence.Equiv_iff_LimZero {a b: ℕ → ℚ} (ha: IsCauchy a) (hb: IsCauchy b)
   : Equiv a b ↔ CauSeq.LimZero (ha.CauSeq - hb.CauSeq) := by
     refine ⟨(·.LimZero ha hb), ?_⟩
     sorry
@@ -182,13 +182,13 @@ theorem Sequence.difference_approaches_zero {a: ℕ → ℚ} (ha: Sequence.IsCau
     sorry
 
 -- There exists a Cauchy sequence entirely above the LIM
-theorem Real.exists_equiv_above {a: ℕ → ℚ} (ha: Sequence.IsCauchy a) 
-  : ∃(b: ℕ → ℚ), Sequence.IsCauchy b ∧ Sequence.Equiv a b ∧ ∀n, LIM a ≤ b n := by 
+theorem Real.exists_equiv_above {a: ℕ → ℚ} (ha: Sequence.IsCauchy a)
+  : ∃(b: ℕ → ℚ), Sequence.IsCauchy b ∧ Sequence.Equiv a b ∧ ∀n, LIM a ≤ b n := by
     sorry
 
 -- There exists a Cauchy sequence entirely below the LIM
-theorem Real.exists_equiv_below {a: ℕ → ℚ} (ha: Sequence.IsCauchy a) 
-  : ∃(b: ℕ → ℚ), Sequence.IsCauchy b ∧ Sequence.Equiv a b ∧ ∀n, b n ≤ LIM a := by 
+theorem Real.exists_equiv_below {a: ℕ → ℚ} (ha: Sequence.IsCauchy a)
+  : ∃(b: ℕ → ℚ), Sequence.IsCauchy b ∧ Sequence.Equiv a b ∧ ∀n, b n ≤ LIM a := by
     sorry
 
 ----
@@ -200,8 +200,8 @@ theorem Real.exists_equiv_below {a: ℕ → ℚ} (ha: Sequence.IsCauchy a)
 
 -- Transform a `Real` to an `ℝ` by going through Cauchy Sequences
 -- we can use the conversion of Real.mk_eq to use different sequences to show different parts
-theorem Real.equivR_eq' {a: ℕ → ℚ} (ha: Sequence.IsCauchy a) 
-  : (LIM a).equivR = Real.mk ha.CauSeq := by 
+theorem Real.equivR_eq' {a: ℕ → ℚ} (ha: Sequence.IsCauchy a)
+  : (LIM a).equivR = Real.mk ha.CauSeq := by
     by_cases hq: ∃(q: ℚ), q = LIM a
     · sorry
     show sSup (Rat.cast '' (LIM a).toSet_Rat) = _
@@ -215,12 +215,12 @@ theorem Real.equivR_eq' {a: ℕ → ℚ} (ha: Sequence.IsCauchy a)
     intro M hM
     sorry
 
-lemma Real.equivR_eq (x: Real) : ∃(a : ℕ → ℚ) (ha: Sequence.IsCauchy a), 
-  x = LIM a ∧ x.equivR = Real.mk ha.CauSeq := by 
+lemma Real.equivR_eq (x: Real) : ∃(a : ℕ → ℚ) (ha: Sequence.IsCauchy a),
+  x = LIM a ∧ x.equivR = Real.mk ha.CauSeq := by
     obtain ⟨a, ha, rfl⟩ := x.eq_lim
     exact ⟨a, ha, rfl, equivR_eq' ha⟩
 
-/-- The isomorphism preserves order and ring operations -/
+/-- The isomorphism preserves order and ring operations. -/
 noncomputable abbrev Real.equivR_ordered_ring : Real ≃+*o ℝ where
   toEquiv := equivR
   map_add' := by sorry
diff --git a/analysis/Analysis/Section_6_1.lean b/Analysis/Section_6_1.lean
similarity index 93%
rename from analysis/Analysis/Section_6_1.lean
rename to Analysis/Section_6_1.lean
index ca5fa4b1..3b6324f4 100644
--- a/analysis/Analysis/Section_6_1.lean
+++ b/Analysis/Section_6_1.lean
@@ -14,7 +14,7 @@ doing so.
 
 Main constructions and results of this section:
 
-- Definition of $ε$-closeness, $ε$-steadiness, and their eventual counterparts.
+- Definition of $`ε`-closeness, $`ε`-steadiness, and their eventual counterparts.
 - Notion of a Cauchy sequence, convergent sequence, and bounded sequence of reals.
 
 -/
@@ -43,7 +43,7 @@ structure Sequence where
   seq : ℤ → ℝ
   vanish : ∀ n < m, seq n = 0
 
-/-- Sequences can be thought of as functions from ℤ to ℝ. -/
+/-- Sequences can be thought of as functions from {lean}`ℤ` to {lean}`ℝ`. -/
 instance Sequence.instCoeFun : CoeFun Sequence (fun _ ↦ ℤ → ℝ) where
   coe a := a.seq
 
@@ -55,7 +55,7 @@ abbrev Sequence.ofNatFun (a:ℕ → ℝ) : Sequence :=
     vanish := by simp_all
  }
 
-/-- Functions from ℕ to ℝ can be thought of as sequences. -/
+/-- Functions from {lean}`ℕ` to {lean}`ℝ` can be thought of as sequences. -/
 instance Sequence.instCoe : Coe (ℕ → ℝ) Sequence where
   coe := ofNatFun
 
@@ -71,8 +71,9 @@ lemma Sequence.eval_mk {n m:ℤ} (a: { n // n ≥ m } → ℝ) (h: n ≥ m) :
 lemma Sequence.eval_coe (n:ℕ) (a: ℕ → ℝ) : (a:Sequence) n = a n := by simp
 
 /--
-  a.from n₁ starts `a:Sequence` from `n₁`.  It is intended for use when `n₁ ≥ n₀`, but returns
-  the "junk" value of the original sequence `a` otherwise.
+  {given -show}`n₁, n₀`
+  {lean}`a.from n₁` starts {lean}`a : Sequence` from {name}`n₁`.  It is intended for use when {lean}`n₁ ≥ n₀`, but returns
+  the "junk" value of the original sequence {name}`a` otherwise.
 -/
 abbrev Sequence.from (a:Sequence) (m₁:ℤ) : Sequence := mk' (max a.m m₁) (a ↑·)
 
@@ -98,11 +99,11 @@ abbrev Real.EventuallySteady (ε: ℝ) (a: Chapter6.Sequence) : Prop :=
 lemma Real.eventuallySteady_def (ε: ℝ) (a: Chapter6.Sequence) :
   ε.EventuallySteady a ↔ ∃ N, (N ≥ a.m) ∧ ε.Steady (a.from N) := by rfl
 
-/-- For fixed s, the function ε ↦ ε.Steady s is monotone -/
+/-- For fixed {name}`a`, the function `ε ↦ ε.Steady s` is monotone -/
 theorem Real.Steady.mono {a: Chapter6.Sequence} {ε₁ ε₂: ℝ} (hε: ε₁ ≤ ε₂) (hsteady: ε₁.Steady a) :
     ε₂.Steady a := by grind
 
-/-- For fixed s, the function ε ↦ ε.EventuallySteady s is monotone -/
+/-- For fixed {name}`a`, the function `ε ↦ ε.EventuallySteady s` is monotone -/
 theorem Real.EventuallySteady.mono {a: Chapter6.Sequence} {ε₁ ε₂: ℝ} (hε: ε₁ ≤ ε₂)
   (hsteady: ε₁.EventuallySteady a) :
     ε₂.EventuallySteady a := by peel 2 hsteady; grind [Steady.mono]
@@ -116,7 +117,7 @@ abbrev Sequence.IsCauchy (a:Sequence) : Prop := ∀ ε > (0:ℝ), ε.EventuallyS
 lemma Sequence.isCauchy_def (a:Sequence) :
   a.IsCauchy ↔ ∀ ε > (0:ℝ), ε.EventuallySteady a := by rfl
 
-/-- This is almost the same as Chapter5.Sequence.IsCauchy.coe -/
+/-- This is almost the same as {name}`Chapter5.Sequence.IsCauchy.coe` -/
 lemma Sequence.IsCauchy.coe (a:ℕ → ℝ) :
     (a:Sequence).IsCauchy ↔ ∀ ε > 0, ∃ N, ∀ j ≥ N, ∀ k ≥ N, dist (a j) (a k) ≤ ε := by
   peel with ε hε
@@ -292,7 +293,7 @@ theorem Sequence.divergent_def (a:Sequence) : a.Divergent ↔ ¬ a.Convergent :=
 
 open Classical in
 /--
-  Definition 6.1.8.  We give the limit of a sequence the junk value of 0 if it is not convergent.
+  Definition 6.1.8.  We give the limit of a sequence the junk value of {lean}`0` if it is not convergent.
 -/
 noncomputable abbrev lim (a:Sequence) : ℝ := if h: a.Convergent then h.choose else 0
 
@@ -394,7 +395,7 @@ theorem Sequence.add_coe (a b: ℕ → ℝ) : (a:Sequence) + (b:Sequence) = (fun
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Theorem 6.1.19(a) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(a) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_add {a b:Sequence} {L M:ℝ} (ha: a.TendsTo L) (hb: b.TendsTo M) :
   (a+b).TendsTo (L+M) := by
@@ -418,7 +419,7 @@ theorem Sequence.mul_coe (a b: ℕ → ℝ) : (a:Sequence) * (b:Sequence) = (fun
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Theorem 6.1.19(b) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(b) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_mul {a b:Sequence} {L M:ℝ} (ha: a.TendsTo L) (hb: b.TendsTo M) :
     (a * b).TendsTo (L * M) := by
@@ -443,7 +444,7 @@ theorem Sequence.smul_coe (c:ℝ) (a:ℕ → ℝ) : (c • (a:Sequence)) = (fun
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h, HSMul.hSMul, SMul.smul]
 
-/-- Theorem 6.1.19(c) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(c) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_smul (c:ℝ) {a:Sequence} {L:ℝ} (ha: a.TendsTo L) :
     (c • a).TendsTo (c * L) := by
@@ -467,7 +468,7 @@ theorem Sequence.sub_coe (a b: ℕ → ℝ) : (a:Sequence) - (b:Sequence) = (fun
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Theorem 6.1.19(d) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(d) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_sub {a b:Sequence} {L M:ℝ} (ha: a.TendsTo L) (hb: b.TendsTo M) :
     (a - b).TendsTo (L - M) := by
@@ -491,7 +492,7 @@ theorem Sequence.inv_coe (a: ℕ → ℝ) : (a:Sequence)⁻¹ = (fun n ↦ (a n)
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Theorem 6.1.19(e) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(e) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_inv {a:Sequence} {L:ℝ} (ha: a.TendsTo L) (hnon: L ≠ 0) :
     (a⁻¹).TendsTo (L⁻¹) := by
@@ -515,7 +516,7 @@ theorem Sequence.div_coe (a b: ℕ → ℝ) : (a:Sequence) / (b:Sequence) = (fun
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Theorem 6.1.19(f) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(f) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_div {a b:Sequence} {L M:ℝ} (ha: a.TendsTo L) (hb: b.TendsTo M) (hnon: M ≠ 0) :
     (a / b).TendsTo (L / M) := by
@@ -539,7 +540,7 @@ theorem Sequence.max_coe (a b: ℕ → ℝ) : (a:Sequence) ⊔ (b:Sequence) = (f
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Theorem 6.1.19(g) (limit laws).  The `tendsTo` version is more usable than the `lim` version
+/-- Theorem 6.1.19(g) (limit laws).  The {name}`Sequence.TendsTo` version is more usable than the {name}`lim` version
     in applications. -/
 theorem Sequence.tendsTo_max {a b:Sequence} {L M:ℝ} (ha: a.TendsTo L) (hb: b.TendsTo M) :
     (max a b).TendsTo (max L M) := by
diff --git a/analysis/Analysis/Section_6_2.lean b/Analysis/Section_6_2.lean
similarity index 97%
rename from analysis/Analysis/Section_6_2.lean
rename to Analysis/Section_6_2.lean
index f2a5dc18..82b47250 100644
--- a/analysis/Analysis/Section_6_2.lean
+++ b/Analysis/Section_6_2.lean
@@ -13,8 +13,8 @@ doing so.
 
 Main constructions and results of this section:
 
-- Some API for Mathlib's extended reals `EReal`, particularly with regard to the supremum
-  operation `sSup` and infimum operation `sInf`.
+- Some API for Mathlib's extended reals {name}`EReal`, particularly with regard to the supremum
+  operation {name}`sSup` and infimum operation {name}`sInf`.
 
 -/
 
@@ -176,7 +176,7 @@ theorem EReal.inf_ge_upper (E: Set EReal) {M:EReal} (hM: M ∈ lowerBounds E) :
 #check isLUB_iff_sSup_eq
 #check isGLB_iff_sInf_eq
 
-/-- Not in textbook: identify the Chapter 5 extended reals with the Mathlib extended reals.
+/-- Not in textbook: identify the Chapter 5 extended reals with the Mathlib {name}`EReal`.
 -/
 noncomputable abbrev Chapter5.ExtendedReal.toEReal (x:ExtendedReal) : EReal := match x with
   | real r => ((Real.equivR r):EReal)
diff --git a/analysis/Analysis/Section_6_3.lean b/Analysis/Section_6_3.lean
similarity index 100%
rename from analysis/Analysis/Section_6_3.lean
rename to Analysis/Section_6_3.lean
diff --git a/analysis/Analysis/Section_6_4.lean b/Analysis/Section_6_4.lean
similarity index 100%
rename from analysis/Analysis/Section_6_4.lean
rename to Analysis/Section_6_4.lean
diff --git a/analysis/Analysis/Section_6_5.lean b/Analysis/Section_6_5.lean
similarity index 100%
rename from analysis/Analysis/Section_6_5.lean
rename to Analysis/Section_6_5.lean
diff --git a/analysis/Analysis/Section_6_6.lean b/Analysis/Section_6_6.lean
similarity index 94%
rename from analysis/Analysis/Section_6_6.lean
rename to Analysis/Section_6_6.lean
index 77704c10..ee6361cb 100644
--- a/analysis/Analysis/Section_6_6.lean
+++ b/Analysis/Section_6_6.lean
@@ -68,8 +68,8 @@ def Sequence.exist_subseq_of_subseq :
     sorry
 
 /--
-  Exercise 6.6.3.  You may find the API around Mathlib's `Nat.find` to be useful
-  (and `open Classical` to avoid any decidability issues)
+  Exercise 6.6.3.  You may find the API around Mathlib's {name}`Nat.find` to be useful
+  (and {syntax command}`open Classical` to avoid any decidability issues)
 -/
 theorem Sequence.subseq_of_unbounded {a:ℕ → ℝ} (ha: ¬ (a:Sequence).IsBounded) :
     ∃ b:ℕ → ℝ, Sequence.subseq a b ∧ (b:Sequence)⁻¹.TendsTo 0 := by
diff --git a/analysis/Analysis/Section_6_7.lean b/Analysis/Section_6_7.lean
similarity index 100%
rename from analysis/Analysis/Section_6_7.lean
rename to Analysis/Section_6_7.lean
diff --git a/analysis/Analysis/Section_6_epilogue.lean b/Analysis/Section_6_epilogue.lean
similarity index 90%
rename from analysis/Analysis/Section_6_epilogue.lean
rename to Analysis/Section_6_epilogue.lean
index 6e33b198..15b9475a 100644
--- a/analysis/Analysis/Section_6_epilogue.lean
+++ b/Analysis/Section_6_epilogue.lean
@@ -5,7 +5,7 @@ import Analysis.Section_6_7
 # Analysis I, Chapter 6 epilogue: Connections with Mathlib limits
 
 In this (technical) epilogue, we show that various operations and properties we have defined for
-"Chapter 6" sequences `Chapter6.Sequence` are equivalent to Mathlib operations.  Note however
+"Chapter 6" sequences {name}`Chapter6.Sequence` are equivalent to Mathlib operations.  Note however
 that Mathlib's operations are defined in far greater generality than the setting of real-valued
 sequences, in particular using the language of filters.
 
@@ -31,7 +31,7 @@ theorem Chapter6.Sequence.Cauchy_iff_CauchySeq (a: ℕ → ℝ) :
   rw [isCauchy_iff_isCauSeq]
   convert isCauSeq_iff_cauchySeq
 
-/-- Identification with `Filter.Tendsto` -/
+/-- Identification with {name}`Filter.Tendsto` -/
 theorem Chapter6.Sequence.tendsto_iff_Tendsto (a: ℕ → ℝ) (L:ℝ) :
     (a:Sequence).TendsTo L ↔ atTop.Tendsto a (nhds L) := by
   rw [Metric.tendsto_atTop, tendsTo_iff]
@@ -56,10 +56,10 @@ theorem Chapter6.Sequence.converges_iff_Tendsto (a: ℕ → ℝ) :
 theorem Chapter6.Sequence.converges_iff_Tendsto' (a: Sequence) :
     a.Convergent ↔ ∃ L, atTop.Tendsto a.seq (nhds L) := by simp_rw [←tendsto_iff_Tendsto']
 
-/-- A technicality: `CauSeq.IsComplete ℝ` was established for `_root_.abs` but not for `norm`. -/
+/-- A technicality: {name}`CauSeq.IsComplete` {lean}`ℝ` was established for {name}`_root_.abs` but not for {name}`norm`. -/
 instance inst_real_complete : CauSeq.IsComplete ℝ norm := by convert Real.instIsCompleteAbs
 
-/-- Identification with `CauSeq.lim` -/
+/-- Identification with {name}`CauSeq.lim` -/
 theorem Chapter6.Sequence.lim_eq_CauSeq_lim (a:ℕ → ℝ) (ha: (a:Sequence).IsCauchy) :
     Chapter6.lim (a:Sequence) = CauSeq.lim  ⟨ a, (isCauchy_iff_isCauSeq a).mp ha⟩ := by
   have h1 := CauSeq.tendsto_limit ⟨ a, (isCauchy_iff_isCauSeq a).mp ha⟩
@@ -67,12 +67,12 @@ theorem Chapter6.Sequence.lim_eq_CauSeq_lim (a:ℕ → ℝ) (ha: (a:Sequence).Is
   rw [←tendsto_iff_Tendsto] at h1
   by_contra! h; apply (a:Sequence).tendsTo_unique at h; tauto
 
-/-- Identification with `limUnder` -/
+/-- Identification with {name}`limUnder` -/
 theorem Chapter6.Sequence.lim_eq_limUnder (a:ℕ → ℝ) (ha: (a:Sequence).Convergent) :
     Chapter6.lim (a:Sequence) = limUnder Filter.atTop a := by
     sorry
 
-/-- Identification with `Bornology.IsBounded` -/
+/-- Identification with {name}`Bornology.IsBounded` -/
 theorem Chapter6.Sequence.isBounded_iff_isBounded_range (a:ℕ → ℝ):
     (a:Sequence).IsBounded ↔ Bornology.IsBounded (Set.range a) := by
   simp [isBounded_def, boundedBy_def, Metric.isBounded_iff]
@@ -108,7 +108,7 @@ theorem Chapter6.Sequence.Monotone_iff (a:ℕ → ℝ): (a:Sequence).IsMonotone
 
 theorem Chapter6.Sequence.Antitone_iff (a:ℕ → ℝ): (a:Sequence).IsAntitone ↔ Antitone a := by sorry
 
-/-- Identification with `MapClusterPt` -/
+/-- Identification with {name}`MapClusterPt` -/
 theorem Chapter6.Sequence.limit_point_iff (a:ℕ → ℝ) (L:ℝ) :
     (a:Sequence).LimitPoint L ↔ MapClusterPt L .atTop a := by
   simp_rw [limit_point_def, mapClusterPt_iff_frequently, frequently_atTop, Metric.mem_nhds_iff]
@@ -124,18 +124,18 @@ theorem Chapter6.Sequence.limit_point_iff (a:ℕ → ℝ) (L:ℝ) :
   refine ⟨ n, by rwa [ge_iff_le, ←Int.toNat_le], ?_ ⟩
   simp [Real.dist_eq, hn] at *; linarith
 
-/-- Identification with `Filter.limsup` -/
+/-- Identification with {name}`Filter.limsup` -/
 theorem Chapter6.Sequence.limsup_eq (a:ℕ → ℝ) :
     (a:Sequence).limsup = atTop.limsup (fun n ↦ (a n:EReal)) := by
   simp_rw [Filter.limsup_eq, eventually_atTop]
   sorry
 
-/-- Identification with `Filter.liminf` -/
+/-- Identification with {name}`Filter.liminf` -/
 theorem Chapter6.Sequence.liminf_eq (a:ℕ → ℝ) :
     (a:Sequence).liminf = atTop.liminf (fun n ↦ (a n:EReal)) := by
   simp_rw [Filter.liminf_eq, eventually_atTop]
   sorry
 
-/-- Identification of `rpow` and Mathlib exponentiation -/
+/-- Identification of {name}`Chapter6.Real.rpow` and Mathlib exponentiation -/
 theorem Chapter6.Real.rpow_eq_rpow {x:ℝ} (hx: x > 0) (α:ℝ) : rpow x α = x^α := by
   sorry
diff --git a/analysis/Analysis/Section_7_1.lean b/Analysis/Section_7_1.lean
similarity index 94%
rename from analysis/Analysis/Section_7_1.lean
rename to Analysis/Section_7_1.lean
index b0ae70c7..c9d6570f 100644
--- a/analysis/Analysis/Section_7_1.lean
+++ b/Analysis/Section_7_1.lean
@@ -1,5 +1,7 @@
 import Mathlib.Tactic
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 7.1: Finite series
 
@@ -20,11 +22,11 @@ Main constructions and results of this section:
 open BigOperators
 
 /-!
-- API for summation over finite sets (encoded using Mathlib's `Finset` type), using the
-  `Finset.sum` method and the `∑ n ∈ A, f n` notation.
+- API for summation over finite sets (encoded using Mathlib's {name}`Finset` type), using the
+  {name}`Finset.sum` method and the `∑ n ∈ A, f n` notation.
 - Fubini's theorem for finite series
 
-We do not attempt to replicate the full API for `Finset.sum` here, but in subsequent sections we
+We do not attempt to replicate the full API for {name}`Finset.sum` here, but in subsequent sections we
 shall make liberal use of this API.
 
 -/
@@ -43,7 +45,7 @@ theorem sum_of_empty {n m:ℤ} (h: n < m) (a: ℤ → ℝ) : ∑ i ∈ Icc m n,
   rw [sum_eq_zero]; intro _; rw [mem_Icc]; grind
 
 /--
-  Definition 7.1.1. This is similar to Mathlib's `Finset.sum_Icc_succ_top` except that the
+  Definition 7.1.1. This is similar to Mathlib's {name}`Finset.sum_Icc_succ_top` except that the
   latter involves summation over the natural numbers rather than integers.
 -/
 theorem sum_of_nonempty {n m:ℤ} (h: n ≥ m-1) (a: ℤ → ℝ) :
@@ -169,7 +171,7 @@ theorem finite_series_of_rearrange {n:ℕ} {X':Type*} (X: Finset X') (hcard: X.c
 
 /--
   This fact ensures that Definition 7.1.6 would be well-defined even if we did not appeal to the
-  existing `Finset.sum` method.
+  existing {name}`Finset.sum` method.
 -/
 theorem exist_bijection {n:ℕ} {Y:Type*} (X: Finset Y) (hcard: X.card = n) :
     ∃ g: Icc (1:ℤ) n → X, Function.Bijective g := by
@@ -294,7 +296,7 @@ theorem finite_series_comm {XX YY:Type*} (X: Finset XX) (Y: Finset YY) (f: XX ×
 
 /--
   Exercise 7.1.4. Note: there may be some technicalities passing back and forth between natural
-  numbers and integers. Look into the tactics `zify`, `norm_cast`, and `omega`
+  numbers and integers. Look into the tactics {tactic}`zify`, {tactic}`norm_cast`, and {tactic}`omega`
 -/
 theorem binomial_theorem (x y:ℝ) (n:ℕ) :
     (x + y)^n
@@ -317,8 +319,8 @@ theorem sum_union_disjoint {n : ℕ} {S : Type*} [Fintype S]
     ∑ s, f s = ∑ i, ∑ s ∈ E i, f s := by
   sorry
 
-/-- Exercise 7.1.7. Uses `Fin m` (so `aᵢ < m`) instead of the book's `aᵢ ≤ m`;
-  the bound is baked into the type, and `<` replaces `≤` to match the 0-indexed shift. -/
+/-- {given}`aᵢ` Exercise 7.1.7. Uses {lean}`Fin m` (so {lean}`aᵢ < m`) instead of the book's {lean}`aᵢ ≤ m`;
+  the bound is baked into the type, and {kw (of := «term_<_»)}`<` replaces {kw (of := «term_≤_»)}`≤` to match the 0-indexed shift. -/
 theorem sum_finite_col_row_counts {n m : ℕ} (a : Fin n → Fin m) :
     ∑ i, (a i : ℕ) = ∑ j : Fin m, {i : Fin n | j < a i}.toFinset.card := by
   sorry
diff --git a/analysis/Analysis/Section_7_2.lean b/Analysis/Section_7_2.lean
similarity index 98%
rename from analysis/Analysis/Section_7_2.lean
rename to Analysis/Section_7_2.lean
index 958aa44e..3e55513f 100644
--- a/analysis/Analysis/Section_7_2.lean
+++ b/Analysis/Section_7_2.lean
@@ -206,7 +206,7 @@ theorem Series.add_coe (a b: ℕ → ℝ) : (a:Series) + (b:Series) = (fun n ↦
   change (a:Series).seq n + (b:Series).seq n = _
   by_cases h:n ≥ 0 <;> simp [h]
 
-/-- Proposition 7.2.14 (a) (Series laws) / Exercise 7.2.5.  The `convergesTo` form can be more convenient for applications. -/
+/-- Proposition 7.2.14 (a) (Series laws) / Exercise 7.2.5.  The {name}`convergesTo` form can be more convenient for applications. -/
 theorem Series.convergesTo.add {s t:Series} {L M: ℝ} (hs: s.convergesTo L) (ht: t.convergesTo M) :
     (s + t).convergesTo (L + M) := by
   sorry
@@ -225,7 +225,7 @@ theorem Series.smul_coe (a: ℕ → ℝ) (c: ℝ) : (c • a:Series) = (fun n 
   ext n; rfl
   by_cases h:n ≥ 0 <;> simp [h, HSMul.hSMul, SMul.smul]
 
-/-- Proposition 7.2.14 (b) (Series laws) / Exercise 7.2.5.  The `convergesTo` form can be more convenient for applications. -/
+/-- Proposition 7.2.14 (b) (Series laws) / Exercise 7.2.5.  The {name}`convergesTo` form can be more convenient for applications. -/
 theorem Series.convergesTo.smul {s:Series} {L c: ℝ} (hs: s.convergesTo L) :
     (c • s).convergesTo (c * L) := by
   sorry
diff --git a/analysis/Analysis/Section_7_3.lean b/Analysis/Section_7_3.lean
similarity index 100%
rename from analysis/Analysis/Section_7_3.lean
rename to Analysis/Section_7_3.lean
diff --git a/analysis/Analysis/Section_7_4.lean b/Analysis/Section_7_4.lean
similarity index 97%
rename from analysis/Analysis/Section_7_4.lean
rename to Analysis/Section_7_4.lean
index 26d81cba..f4fe0f66 100644
--- a/analysis/Analysis/Section_7_4.lean
+++ b/Analysis/Section_7_4.lean
@@ -1,6 +1,5 @@
 import Mathlib.Tactic
 import Analysis.Section_7_3
-
 /-!
 # Analysis I, Section 7.4: Rearrangement of series
 
@@ -207,8 +206,11 @@ theorem Series.ex_7_4_4'_sum : (fun n ↦ a_7_4_4 (f_7_4_4 n) :Series).sum < 0 :
 theorem Series.absConverges_of_subseries {a:ℕ → ℝ} (ha: (a:Series).absConverges) {f: ℕ → ℕ} (hf: StrictMono f) :
   (fun n ↦ a (f n):Series).absConverges := by sorry
 
-/-- Exercise 7.4.2 : reprove Proposition 7.4.3 using Proposition 7.41, Proposition 7.2.14,
-    and expressing `a n` as the difference of `a n + |a n|` and `|a n|`. -/
+/--
+{given -show}`n : ℕ`
+Exercise 7.4.2 : reprove Proposition 7.4.3 using Proposition 7.41, Proposition 7.2.14,
+and expressing {lean}`a n` as the difference of {lean}`a n + |a n|` and {lean}`|a n|`.
+-/
 theorem Series.absConverges_of_permute' {a:ℕ → ℝ} (ha : (a:Series).absConverges)
   {f: ℕ → ℕ} (hf: Function.Bijective f) :
     (fun n ↦ a (f n):Series).absConverges  ∧ (a:Series).sum = (fun n ↦ a (f n):Series).sum := by sorry
diff --git a/analysis/Analysis/Section_7_5.lean b/Analysis/Section_7_5.lean
similarity index 100%
rename from analysis/Analysis/Section_7_5.lean
rename to Analysis/Section_7_5.lean
diff --git a/analysis/Analysis/Section_8_1.lean b/Analysis/Section_8_1.lean
similarity index 97%
rename from analysis/Analysis/Section_8_1.lean
rename to Analysis/Section_8_1.lean
index 35766d7d..9027b74f 100644
--- a/analysis/Analysis/Section_8_1.lean
+++ b/Analysis/Section_8_1.lean
@@ -12,7 +12,7 @@ doing so.
 Main constructions and results of this section:
 
 - Custom notions for "equal cardinality", "countable", and "at most countable".  Note that Mathlib's
-`Countable` typeclass corresponds to what we call "at most countable" in this text.
+{name}`Countable` typeclass corresponds to what we call "at most countable" in this text.
 - Countability of the integers and rationals.
 
 Note that as the Chapter 3 set theory has been deprecated, we will not re-use relevant constructions from that theory here, replacing them with Mathlib counterparts instead.
@@ -26,13 +26,13 @@ This is analogous to `Chapter3.SetTheory.Set.EqualCard`, but we are not using th
 the Chapter 3 set theory is deprecated. -/
 abbrev EqualCard (X Y : Type) : Prop := ∃ f : X → Y, Function.Bijective f
 
-/-- Relation with Mathlib's `Equiv` concept -/
+/-- Relation with Mathlib's {name}`Equiv` concept -/
 theorem EqualCard.iff {X Y : Type} : EqualCard X Y ↔ Nonempty (X ≃ Y) := by
   simp [EqualCard]; constructor
   . intro ⟨ f, hf ⟩; exact ⟨ .ofBijective f hf ⟩
   intro ⟨ e ⟩; exact ⟨ e.toFun, e.bijective ⟩
 
-/-- Equivalence with Mathlib's `Cardinal.mk` concept -/
+/-- Equivalence with Mathlib's {name}`Cardinal.mk` concept -/
 theorem EqualCard.iff' {X Y : Type} : EqualCard X Y ↔ Cardinal.mk X = Cardinal.mk Y := by
   simp [Cardinal.eq, iff]
 
@@ -64,13 +64,13 @@ theorem AtMostCountable.equiv {X Y: Type} (hXY : EqualCard X Y) :
   AtMostCountable X ↔ AtMostCountable Y := by
   simp [AtMostCountable, CountablyInfinite.equiv hXY, Finite.equiv hXY]
 
-/-- Equivalence with Mathlib's `Denumerable` concept (cf. Remark 8.1.2) -/
+/-- Equivalence with Mathlib's {name}`Denumerable` concept (cf. Remark 8.1.2) -/
 theorem CountablyInfinite.iff (X : Type) : CountablyInfinite X ↔ Nonempty (Denumerable X) := by
   simp [CountablyInfinite, EqualCard.iff]; constructor
   . intro ⟨ e ⟩; exact ⟨ Denumerable.mk' e ⟩
   intro ⟨ h ⟩; exact ⟨ h.eqv X ⟩
 
-/-- Equivalence with Mathlib's `Countable` typeclass -/
+/-- Equivalence with Mathlib's {name}`Countable` typeclass -/
 theorem CountablyInfinite.iff' (X : Type) : CountablyInfinite X ↔ Countable X ∧ Infinite X := by
   rw [iff, nonempty_denumerable_iff]
 
@@ -141,7 +141,7 @@ theorem Nat.min_eq_sInf {X : Set ℕ} (hX : X.Nonempty) : min X = sInf X := by
   sorry
 
 open Classical in
-/-- Equivalence with Mathlib's `Nat.find` method -/
+/-- Equivalence with Mathlib's {name}`Nat.find` method -/
 theorem Nat.min_eq_find {X : Set ℕ} (hX : X.Nonempty) : min X = Nat.find hX := by
   symm; rw [Nat.find_eq_iff]; have := min_spec hX; grind
 
@@ -319,7 +319,7 @@ example (A: Type) : AtMostCountable A ↔ ∃ f : A → ℕ, Function.Injective
 example {I X:Type} (hI: AtMostCountable I) (A: I → Set X) (hA: ∀ i, AtMostCountable (A i)) :
   AtMostCountable (⋃ i, A i) := by sorry
 
-/-- Exercise 8.1.10.  Note the lack of the `noncomputable` keyword in the `abbrev`. -/
+/-- Exercise 8.1.10.  Note the lack of the `noncomputable` keyword in the {lit}`abbrev`. -/
 abbrev explicit_bijection : ℕ → ℚ := sorry
 
 theorem explicit_bijection_spec : Function.Bijective explicit_bijection := by sorry
diff --git a/analysis/Analysis/Section_8_2.lean b/Analysis/Section_8_2.lean
similarity index 96%
rename from analysis/Analysis/Section_8_2.lean
rename to Analysis/Section_8_2.lean
index 99383707..3654832d 100644
--- a/analysis/Analysis/Section_8_2.lean
+++ b/Analysis/Section_8_2.lean
@@ -16,13 +16,13 @@ doing so.
 Main constructions and results of this section:
 
 - Absolute convergence and summation on countably infinite or general sets.
-- Connections with Mathlib's `Summable` and `tsum`.
+- Connections with Mathlib's {name}`Summable` and {name}`tsum`.
 - The Riemann rearrangement theorem.
 
 Some non-trivial API is provided beyond what is given in the textbook in order connect these
 notions with existing summation notions.
 
-After this section, the summation notation developed here will be deprecated in favor of Mathlib's API for `Summable` and `tsum`.
+After this section, the summation notation developed here will be deprecated in favor of Mathlib's API for {name}`Summable` and {name}`tsum`.
 
 -/
 
@@ -30,15 +30,15 @@ namespace Chapter8
 open Chapter7 Chapter7.Series Finset Function Filter
 
 /-- Definition 8.2.1 (Series on countable sets).  Note that with this definition, functions defined
-on finite sets will not be absolutely convergent; one should use `AbsConvergent'` instead for such
+on finite sets will not be absolutely convergent; one should use {lit}`AbsConvergent'` instead for such
 cases.-/
 abbrev AbsConvergent {X:Type} (f: X → ℝ) : Prop := ∃ g: ℕ → X, Bijective g ∧ (f ∘ g: Series).absConverges
 
 theorem AbsConvergent.mk {X: Type} {f:X → ℝ} {g:ℕ → X} (h: Bijective g) (hfg: (f ∘ g:Series).absConverges) : AbsConvergent f := by use g
 
 open Classical in
-/-- The definition has been chosen to give a sensible value when `X` is finite, even though
-`AbsConvergent` is by definition false in this context. -/
+/-- The definition has been chosen to give a sensible value when {name}`X` is finite, even though
+{name}`AbsConvergent` is by definition false in this context. -/
 noncomputable abbrev Sum {X:Type} (f: X → ℝ) : ℝ := if h: AbsConvergent f then (f ∘ h.choose:Series).sum else
   if _hX: Finite X then (∑ x ∈ @univ X (Fintype.ofFinite X), f x) else 0
 
@@ -240,14 +240,14 @@ theorem AbsConvergent'.countable_supp {X:Type} {f:X → ℝ} (hf: AbsConvergent'
   AtMostCountable { x | f x ≠ 0 } := by
     sorry
 
-/-- Compare with Mathlib's `Summable.subtype`-/
+/-- Compare with Mathlib's {name}`Summable.subtype`-/
 theorem AbsConvergent'.subtype {X:Type} {f:X → ℝ} (hf: AbsConvergent' f) (A: Set X) :
   AbsConvergent' (fun x:A ↦ f x) := by
   apply BddAbove.mono _ hf
   intro z hz; simp at *; choose A hA using hz
   use A.map (Embedding.subtype _); simp [hA]
 
-/-- A generalized sum.  Note that this will give junk values if `f` is not `AbsConvergent'`. -/
+/-- A generalized sum.  Note that this will give junk values if {name}`f` is not {name}`AbsConvergent'`. -/
 noncomputable abbrev Sum' {X:Type} (f: X → ℝ) : ℝ := Sum (fun x : { x | f x ≠ 0 } ↦ f x)
 
 /-- Not in textbook, but should have been included (the series laws are significantly harder
@@ -337,7 +337,7 @@ theorem Sum'.of_countable_supp {X:Type} {f:X → ℝ} {A: Set X} (hA: CountablyI
     _ = ∑ n, f (ι n) := sum_congr rfl (by grind)
     _ = _ := hι.sum_comp (g := fun x ↦ f x)
 
-/-- Connection with Mathlib's `Summable` property. Some version of this might be suitable
+/-- Connection with Mathlib's {name}`Summable` property. Some version of this might be suitable
     for Mathlib? -/
 theorem AbsConvergent'.iff_Summable {X:Type} (f:X → ℝ) : AbsConvergent' f ↔ Summable f := by
   simp [←summable_abs_iff, AbsConvergent']
@@ -352,7 +352,7 @@ theorem AbsConvergent'.iff_Summable {X:Type} (f:X → ℝ) : AbsConvergent' f 
     use S; intro T hT
     rw [abs_of_nonneg (by positivity)]
     have : ∑ x ∈ T, |f x| + ∑ x ∈ S, |f x| ≤ sSup s := by
-      apply ConditionallyCompleteLattice.le_csSup _ _ h
+      apply le_csSup h
       simp [s]; exact ⟨ T ∪ S, sum_union hT ⟩
     linarith
   intro h; choose S hS using h 1 (by norm_num)
@@ -382,7 +382,7 @@ atTop.Tendsto f l ↔ atTop.Tendsto (f ∘ Nat.cast) l := by
   convert Eventually.int_natCast_atTop _
 
 
-/-- Connection with Mathlib's `tsum` (or `Σ'`) operation -/
+/-- Connection with Mathlib's {name}`tsum` (or {kw (of := «termΣ'_,_»)}`Σ'`) operation -/
 theorem Sum'.eq_tsum {X:Type} (f:X → ℝ) (h: AbsConvergent' f) :
   Sum' f = ∑' x, f x := by
   set E := {x | f x ≠ 0}
@@ -428,12 +428,12 @@ theorem Sum'.sub {X:Type} {f g:X → ℝ} (hf: AbsConvergent' f) (hg: AbsConverg
   rw [(smul hg (-1)).2]; ring
 
 /-- Proposition 8.2.6 (c) (Absolutely convergent series laws) / Exercise 8.2.3.  The first
-    part of this proposition has been moved to `AbsConvergent'.subtype`. -/
+    part of this proposition has been moved to {lean}`AbsConvergent'.subtype`. -/
 theorem Sum'.of_disjoint_union {X:Type} {f:X → ℝ} (hf: AbsConvergent' f) {X₁ X₂ : Set X} (hdisj: Disjoint X₁ X₂):
   Sum' (fun x: (X₁ ∪ X₂: Set X) ↦ f x) = Sum' (fun x : X₁ ↦ f x) + Sum' (fun x : X₂ ↦ f x) := by
   sorry
 
-/-- This technical claim, the analogue of `tsum_univ`, is required due to the way Mathlib handles
+/-- This technical claim, the analogue of {name}`tsum_univ`, is required due to the way Mathlib handles
     sets.-/
 theorem Sum'.of_univ {X:Type} {f:X → ℝ} (hf: AbsConvergent' f) :
   Sum' (fun x: (.univ : Set X) ↦ f x) = Sum' f := by
diff --git a/analysis/Analysis/Section_8_3.lean b/Analysis/Section_8_3.lean
similarity index 98%
rename from analysis/Analysis/Section_8_3.lean
rename to Analysis/Section_8_3.lean
index 4734be05..5a6c1be6 100644
--- a/analysis/Analysis/Section_8_3.lean
+++ b/Analysis/Section_8_3.lean
@@ -161,7 +161,7 @@ example {X:Type} [Finite X] : Nat.card (Set X) = 2 ^ Nat.card X := by
   sorry
 
 open Classical in
-/-- Exercise 8.3.2.  Some subtle type changes due to how sets are implemented in Mathlib. Also we shift the sequence `D` by one so that we can work in `Set A` rather than `Set B`. -/
+/-- Exercise 8.3.2.  Some subtle type changes due to how sets are implemented in Mathlib. Also we shift the sequence {lit}`D` by one so that we can work in {lean}`Set A` rather than {lean}`Set B`. -/
 theorem Schroder_Bernstein_lemma {X: Type} {A B C: Set X} (hAB: A ⊆ B) (hBC: B ⊆ C) (f: C ↪ A) :
   let D : ℕ → Set A := Nat.rec ((f.image ∘ ((B.embeddingOfSubset _ hBC).image)) {x:B | ↑x ∉ A}) (fun _ ↦ (f.image ∘ ((B.embeddingOfSubset _ hBC).image) ∘ (A.embeddingOfSubset _ hAB).image))
   Set.univ.PairwiseDisjoint D ∧
diff --git a/analysis/Analysis/Section_8_4.lean b/Analysis/Section_8_4.lean
similarity index 89%
rename from analysis/Analysis/Section_8_4.lean
rename to Analysis/Section_8_4.lean
index b538f414..aa05cb33 100644
--- a/analysis/Analysis/Section_8_4.lean
+++ b/Analysis/Section_8_4.lean
@@ -2,6 +2,8 @@ import Mathlib.Tactic
 import Analysis.Section_8_1
 import Analysis.Section_8_2
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 8.4: The axiom of choice
 
@@ -19,8 +21,8 @@ Main constructions and results of this section:
 As the Chapter 3 set theory has been deprecated for many chapters at this point, we will not insert the axiom of choice directly into that theory in this text; but this could be accomplished if desired
 (e.g., by extending the `Chapter3.SetTheory` class to a `Chapter3.SetTheoryWithChoice` class), and
 students are welcome to attempt this separately.  Instead, we will use Mathlib's native
-`Classical.choice` axiom.  Technically, this axiom has already been used quite frequently in the
-text already, in large part because Mathlib uses `Classical.choice` to derive many weaker statements,
+{name}`Classical.choice` axiom.  Technically, this axiom has already been used quite frequently in the
+text already, in large part because Mathlib uses {name}`Classical.choice` to derive many weaker statements,
 such as the law of the excluded middle.  So the distinctions made in the original text regarding
 whether a given statement or not uses the axiom of choice are somewhat blurred in this formalization.
 It is theoretically possible to restore this distinction by removing the reliance on Mathlib and
@@ -31,11 +33,12 @@ working throughout with custom structures such as `Chapter3.SetTheory` and
 namespace Chapter8
 
 /-- Definition 8.4.1 (Infinite Cartesian products).  We will avoid using this definition in favor
-of the Mathlib form `∀ α, X α` which we will shortly show is equivalent to (or more precisely,
+of the Mathlib form {lean}`∀ α, X α` which we will shortly show is equivalent to (or more precisely,
 generalizes) this one.
 
+{given -show}`α : I`
 Because Lean does not allow unrestricted unions of types, we cheat slightly here by assuming all the
-`X α` are sets in a common universe `U`.  Note that the Mathlib definition does not have this
+{lean}`X α` are sets in a common universe {name}`U`.  Note that the Mathlib definition does not have this
 restriction. -/
 abbrev CartesianProduct {I U: Type} (X : I → Set U) := { x : I → ⋃ α, X α // ∀ α, ↑(x α) ∈ X α }
 
@@ -106,7 +109,7 @@ theorem exist_tendsTo_sup {E: Set ℝ} (hnon: E.Nonempty) (hbound: BddAbove E) :
     have : 1 / (n+1:ℝ) > 0 := by positivity
     choose s hs using (lt_csSup_iff hbound hnon).mp (show sSup E - 1 / (n+1:ℝ) < sSup E by linarith)
     use s; simp_all [X]
-    refine ⟨ by linarith, ConditionallyCompleteLattice.le_csSup _ _ hbound hs.1 ⟩
+    refine ⟨ by linarith, le_csSup hbound hs.1 ⟩
   have ⟨ a ⟩ := axiom_of_countable_choice hX
   use fun n ↦ ↑(a n); constructor; swap
   apply Filter.Tendsto.squeeze (g := fun n:ℕ ↦ sSup E - 1/(n+1:ℝ)) (h := fun _:ℕ ↦ sSup E)
@@ -124,7 +127,7 @@ theorem exist_tendsTo_sup_of_closed {E: Set ℝ} (hnon: E.Nonempty) (hbound: Bdd
     have : 1 / (n+1:ℝ) > 0 := by positivity
     choose s hs using (lt_csSup_iff hbound hnon).mp (show sSup E - 1 / (n+1:ℝ) < sSup E by linarith)
     use s; simp_all [X]
-    refine ⟨ by linarith, ConditionallyCompleteLattice.le_csSup _ _ hbound hs.1 ⟩
+    refine ⟨ by linarith, le_csSup hbound hs.1 ⟩
   set a : ℕ → ℝ := fun n ↦ sInf (X n)
   have ha (n:ℕ) : a n ∈ X n := by
     apply IsClosed.csInf_mem _ Set.Nonempty.of_subtype
@@ -144,7 +147,7 @@ theorem exists_function {X Y : Type} {P : X → Y → Prop} (h: ∀ x, ∃ y, P
   sorry
 
 /-- Exercise 8.4.1.  The spirit of the question here is to establish this result directly
-from `exists_function`, avoiding previous results that relied more explicitly
+from {name}`exists_function`, avoiding previous results that relied more explicitly
 on the axiom of choice. -/
 theorem axiom_of_choice_from_exists_function {I: Type} {X: I → Type} (h : ∀ i, Nonempty (X i)) :
   Nonempty (∀ i, X i) := by
@@ -157,7 +160,7 @@ theorem exists_set_singleton_intersect {I U:Type} {X: I → Set U} (h: Set.Pairw
   sorry
 
 /-- Exercise 8.4.2.  The spirit of the question here is to establish this result directly
-from `exists_set_singleton_intersect`, avoiding previous results that relied more explicitly
+from {name}`exists_set_singleton_intersect`, avoiding previous results that relied more explicitly
 on the axiom of choice. -/
 theorem axiom_of_choice_from_exists_set_singleton_intersect {I: Type} {X: I → Type} (h : ∀ i, Nonempty (X i)) :
   Nonempty (∀ i, X i) := by
@@ -169,7 +172,7 @@ theorem Function.Injective.inv_surjective {A B:Type} {g: B → A} (hg: Function.
   sorry
 
 /-- Exercise 8.4.3.  The spirit of the question here is to establish this result directly
-from `Function.Injective.inv_surjective`, avoiding previous results that relied more explicitly
+from {name}`Function.Injective.inv_surjective`, avoiding previous results that relied more explicitly
 on the axiom of choice. -/
 theorem axiom_of_choice_from_function_injective_inv_surjective {I: Type} {X: I → Type} (h : ∀ i, Nonempty (X i)) :
   Nonempty (∀ i, X i) := by
diff --git a/analysis/Analysis/Section_8_5.lean b/Analysis/Section_8_5.lean
similarity index 95%
rename from analysis/Analysis/Section_8_5.lean
rename to Analysis/Section_8_5.lean
index 5c890c20..f0be6d98 100644
--- a/analysis/Analysis/Section_8_5.lean
+++ b/Analysis/Section_8_5.lean
@@ -1,6 +1,8 @@
 import Mathlib.Tactic
 import Analysis.Section_8_4
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 8.5: Ordered sets
 
@@ -12,7 +14,7 @@ doing so.
 
 Main constructions and results of this section:
 
-- Review of `PartialOrder`, `LinearOrder`, and `WellFoundedLT`, with some API.
+- Review of {name}`PartialOrder`, {name}`LinearOrder`, and {name}`WellFoundedLT`, with some API.
 - Strong induction.
 - Zorn's lemma.
 
@@ -20,7 +22,7 @@ Main constructions and results of this section:
 
 namespace Chapter8
 
-/-- Definition 8.5.1 - Here we just review the Mathlib `PartialOrder` class. -/
+/-- Definition 8.5.1 - Here we just review the Mathlib {name}`PartialOrder` class. -/
 
 example {X:Type} [PartialOrder X] (x:X) : x ≤ x := le_refl x
 example {X:Type} [PartialOrder X] {x y:X} (h₁: x ≤ y) (h₂: y ≤ x) : x = y := antisymm h₁ h₂
@@ -41,7 +43,7 @@ example {X:Type} [PartialOrder X] (x y:X) : x < y ↔ x ≤ y ∧ x ≠ y := lt_
 example {X:Type} : PartialOrder (Set X) := by infer_instance
 example {X:Type} (A B: Set X) : A ≤ B ↔ A ⊆ B := by rfl
 
-/-- Definition 8.5.3.  Here we just review the Mathlib `LinearOrder` class. -/
+/-- Definition 8.5.3.  Here we just review the Mathlib {name}`LinearOrder` class. -/
 example {X:Type} [LinearOrder X] : PartialOrder X := by infer_instance
 def IsTotal (X:Type) [PartialOrder X] : Prop := ∀ x y:X, x ≤ y ∨ y ≤ x
 example {X:Type} [LinearOrder X] : IsTotal X := le_total
@@ -55,10 +57,10 @@ open Classical in
 }
 
 /- Examples 8.5.4 -/
-#check inferInstanceAs (LinearOrder ℕ)
-#check inferInstanceAs (LinearOrder ℚ)
-#check inferInstanceAs (LinearOrder ℝ)
-#check inferInstanceAs (LinearOrder EReal)
+#check (inferInstance : LinearOrder ℕ)
+#check (inferInstance : LinearOrder ℚ)
+#check (inferInstance : LinearOrder ℝ)
+#check (inferInstance : LinearOrder EReal)
 
 
 @[implicit_reducible] noncomputable def LinearOrder.subtype {X:Type} [LinearOrder X] (A: Set X) : LinearOrder A :=
@@ -77,7 +79,7 @@ theorem IsTotal.subset {X:Type} [PartialOrder X] {A B: Set X} (hA: IsTotal A) (h
 abbrev X_8_5_4 : Set (Set ℕ) := { {1,2}, {2}, {2,3}, {2,3,4}, {5} }
 example : ¬ IsTotal X_8_5_4 := by sorry
 
-/-- Definition 8.5.5 (Maximal and minimal elements).  Here we use Mathlib's `IsMax` and `IsMin`. -/
+/-- Definition 8.5.5 (Maximal and minimal elements).  Here we use Mathlib's {name}`IsMax` and {name}`IsMin`. -/
 theorem IsMax.iff {X:Type} [PartialOrder X] (x:X) :
   IsMax x ↔ ¬ ∃ y, x < y := by rw [isMax_iff_forall_not_lt]; grind
 
@@ -150,7 +152,7 @@ theorem WellFoundedLT.strong_induction {X:Type} [LinearOrder X] [WellFoundedLT X
 abbrev IsUpperBound {X:Type} [PartialOrder X] (A:Set X) (x:X) : Prop :=
   ∀ y ∈ A, y ≤ x
 
-/-- Connection with Mathlib's `upperBounds` -/
+/-- Connection with Mathlib's {name}`upperBounds` -/
 theorem IsUpperBound.iff {X:Type} [PartialOrder X] (A:Set X) (x:X) :
   IsUpperBound A x ↔ x ∈ upperBounds A := by simp [IsUpperBound, upperBounds]
 
@@ -170,7 +172,7 @@ example : ¬ IsStrictUpperBound (.Icc 1 2: Set ℝ) 2 := by sorry
 
 example : IsStrictUpperBound (.Icc 1 2: Set ℝ) 3 := by sorry
 
-/-- A convenient way to simplify the notion of having `x₀` as a minimal element.-/
+/-- A convenient way to simplify the notion of having {name}`x₀` as a minimal element.-/
 theorem IsMin.iff_lowerbound {X:Type} [PartialOrder X] {Y: Set X} (hY: IsTotal Y) (x₀ : X) : (∃ hx₀ : x₀ ∈ Y, IsMin (⟨ x₀, hx₀ ⟩:Y)) ↔ x₀ ∈ Y ∧ ∀ x ∈ Y, x₀ ≤ x := by
   constructor
   . rintro ⟨ hx₀, hmin ⟩; simp [IsMin, hx₀] at *
@@ -364,7 +366,7 @@ example {Y:Type} [PartialOrder Y] {x y:Y} (hx: IsMax x) (hy: IsMax y) : x = y :=
 example {X:Type} [LinearOrder X] (hmin: ∀ Y: Set X, Y.Nonempty → ∃ x:Y, IsMin x) (hmax: ∀ Y: Set X, Y.Nonempty → ∃ x:Y, IsMax x) : Finite X := by sorry
 
 
-/-- Exercise 8.5.12.  Here we make a copy of Mathlib's `Lex` wrapper for lexicographical orderings.  This wrapper is needed
+/-- Exercise 8.5.12.  Here we make a copy of Mathlib's {name}`Lex` wrapper for lexicographical orderings.  This wrapper is needed
 because products `X × Y` of ordered sets are given the default instance of the product partial order instead of
 the lexicographical one. -/
 def Lex' (α : Type) := α
diff --git a/analysis/Analysis/Section_9_1.lean b/Analysis/Section_9_1.lean
similarity index 98%
rename from analysis/Analysis/Section_9_1.lean
rename to Analysis/Section_9_1.lean
index 14308e4b..3720a2f7 100644
--- a/analysis/Analysis/Section_9_1.lean
+++ b/Analysis/Section_9_1.lean
@@ -1,7 +1,6 @@
 import Mathlib.Tactic
 import Mathlib.Analysis.SpecificLimits.Basic
 import Analysis.Section_6_4
-
 /-!
 # Analysis I, Section 9.1: Subsets of the real line
 
@@ -86,7 +85,7 @@ theorem closure_def (X:Set ℝ) : closure X = { x | AdherentPt x X } := by
 theorem closure_def' (X:Set ℝ) (x :ℝ) : x ∈ closure X ↔ AdherentPt x X := by
   simp [closure_def]
 
-/-- identification of `AdherentPt` with Mathlib's `ClusterPt` -/
+/-- identification of {name}`AdherentPt` with Mathlib's {name}`ClusterPt` -/
 theorem AdherentPt_def (x:ℝ) (X:Set ℝ) : AdherentPt x X = ClusterPt x (.principal X) := by
   rw [←closure_def', mem_closure_iff_clusterPt]
 
@@ -224,7 +223,7 @@ theorem isClosed_iff_limits_mem (X: Set ℝ) :
 /-- Definition 9.1.18 (Limit points) -/
 abbrev LimitPt (x:ℝ) (X: Set ℝ) := AdherentPt x (X \ {x})
 
-/-- Identification with Mathlib's `AccPt`-/
+/-- Identification with Mathlib's {name}`AccPt`-/
 theorem LimitPt.iff_AccPt (x:ℝ) (X: Set ℝ) : LimitPt x X ↔ AccPt x (.principal X) := by
   rw [accPt_principal_iff_clusterPt,←AdherentPt_def]
 
@@ -288,7 +287,7 @@ theorem mem_Iio_isLimit {a x:ℝ} (hx: x ∈ Set.Iio a) : LimitPt x (.Iio a) :=
 theorem mem_R_isLimit {x:ℝ} : LimitPt x (.univ) := by
   sorry
 
-/-- Definition 9.1.22.  We use here Mathlib's `Bornology.IsBounded`-/
+/-- Definition 9.1.22.  We use here Mathlib's {name}`Bornology.IsBounded`-/
 
 theorem isBounded_def (X: Set ℝ) : Bornology.IsBounded X ↔ ∃ M > 0, X ⊆ .Icc (-M) M := by
   simp [isBounded_iff_forall_norm_le]
@@ -363,7 +362,7 @@ example {X:Set ℝ} (hX: X ≠ ∅) : Bornology.IsBounded X ↔
 example {X:Set ℝ} (hX: Bornology.IsBounded X) : Bornology.IsBounded (closure X) := by
   sorry
 
-/-- Exercise 9.1.12.  As a followup: prove or disprove this exercise with `[Fintype I]` removed. -/
+/-- Exercise 9.1.12.  As a followup: prove or disprove this exercise with {lean}`[Fintype I]` removed. -/
 example {I:Type} [Fintype I] (X: I → Set ℝ) (hX: ∀ i, Bornology.IsBounded (X i)) :
   Bornology.IsBounded (⋃ i, X i) := by
   sorry
diff --git a/analysis/Analysis/Section_9_10.lean b/Analysis/Section_9_10.lean
similarity index 94%
rename from analysis/Analysis/Section_9_10.lean
rename to Analysis/Section_9_10.lean
index d1546cb9..0796617a 100644
--- a/analysis/Analysis/Section_9_10.lean
+++ b/Analysis/Section_9_10.lean
@@ -1,5 +1,4 @@
 import Mathlib.Tactic
-
 /-!
 # Analysis I, Section 9.10: Limits at infinity
 
@@ -15,7 +14,7 @@ Main constructions and results of this section:
 
 namespace Chapter9
 
-/-- Definition 9.10.1 (Infinite adherent point).  We use `¬ BddAbove X` as our notation for `+∞` being an adherent point -/
+/-- Definition 9.10.1 (Infinite adherent point).  We use {lean}`¬ BddAbove X` as our notation for `+∞` being an adherent point -/
 theorem BddAbove.unbounded_iff (X:Set ℝ) : ¬ BddAbove X ↔ ∀ M, ∃ x ∈ X, x > M := by
   simp [bddAbove_def]
 
diff --git a/analysis/Analysis/Section_9_2.lean b/Analysis/Section_9_2.lean
similarity index 100%
rename from analysis/Analysis/Section_9_2.lean
rename to Analysis/Section_9_2.lean
diff --git a/analysis/Analysis/Section_9_3.lean b/Analysis/Section_9_3.lean
similarity index 96%
rename from analysis/Analysis/Section_9_3.lean
rename to Analysis/Section_9_3.lean
index e3e804c6..41160917 100644
--- a/analysis/Analysis/Section_9_3.lean
+++ b/Analysis/Section_9_3.lean
@@ -2,6 +2,8 @@ import Mathlib.Tactic
 import Mathlib.Data.Real.Sign
 import Analysis.Section_9_1
 
+set_option doc.verso.suggestions false
+
 /-!
 # Analysis I, Section 9.3: Limiting values of functions
 
@@ -17,11 +19,11 @@ Main constructions and results of this section:
 - Connection with Mathilb's filter convergence concepts
 - Limit laws for functions
 
-Technical point: in the text, the functions `f` studied are defined only on subsets `X` of `ℝ`, and
+Technical point: in the text, the functions `f` studied are defined only on subsets `X` of {lean}`ℝ`, and
 left undefined elsewhere.  However, in Lean, this then creates some fiddly conversions when trying
-to restrict `f` to various subsets of `X` (which, technically, are not precisely subsets of `ℝ`,
+to restrict `f` to various subsets of `X` (which, technically, are not precisely subsets of {lean}`ℝ`,
 though they can be coerced to such).  To avoid this issue we will deviate from the text by having
-our functions defined on all of `ℝ` (with the understanding that they are assigned "junk" values
+our functions defined on all of {lean}`ℝ` (with the understanding that they are assigned "junk" values
 outside of the domain `X` of interest).
 -/
 
@@ -195,7 +197,7 @@ theorem Convergesto.local {E:Set ℝ} {f: ℝ → ℝ} {L:ℝ} {x₀:ℝ} (h: Ad
   Convergesto E f L x₀ ↔ Convergesto (E ∩ .Ioo (x₀-δ) (x₀+δ)) f L x₀ := by
     sorry
 
-/-- Example 9.3.19.  The point of this example is somewhat blunted by the ability to remove the hypothesis that `g` is non-zero from the relevant part of Proposition 9.3.14 -/
+/-- Example 9.3.19.  The point of this example is somewhat blunted by the ability to remove the hypothesis that {lit}`g` is non-zero from the relevant part of Proposition 9.3.14 -/
 example : Convergesto .univ (fun x ↦ (x+2)/(x+1)) (4/3:ℝ) 2 := by sorry
 
 /-- Example 9.3.20 -/
diff --git a/analysis/Analysis/Section_9_4.lean b/Analysis/Section_9_4.lean
similarity index 96%
rename from analysis/Analysis/Section_9_4.lean
rename to Analysis/Section_9_4.lean
index d3c9db0c..35affd11 100644
--- a/analysis/Analysis/Section_9_4.lean
+++ b/Analysis/Section_9_4.lean
@@ -2,7 +2,6 @@ import Mathlib.Tactic
 import Mathlib.Data.Real.Sign
 import Mathlib.Topology.ContinuousOn
 import Analysis.Section_9_3
-
 /-!
 # Analysis I, Section 9.4: Continuous functions
 
@@ -19,7 +18,9 @@ Main constructions and results of this section:
 
 namespace Chapter9
 
-/-- Definition 9.4.1.  Here we use the Mathlib definition of continuity.  The hypothesis `x ∈ X` is not needed! -/
+/--
+Definition 9.4.1.  Here we use the Mathlib definition of continuity.  The hypothesis {lean}`x₀ ∈ X` is not needed!
+-/
 theorem ContinuousWithinAt.iff (X:Set ℝ) (f: ℝ → ℝ)  (x₀:ℝ) :
   ContinuousWithinAt f X x₀ ↔ Convergesto X f (f x₀) x₀ := by
   rw [ContinuousWithinAt.eq_1, Convergesto.iff, nhdsWithin.eq_1]
@@ -57,7 +58,7 @@ example : ¬ ContinuousAt f_9_4_6 0 := by sorry
 
 example : ContinuousWithinAt f_9_4_6 (.Ici 0) 0 := by sorry
 
-/-- Proposition 9.4.7 / Exercise 9.4.1.  It is possible that the hypothesis `x₀ ∈ X` is unnecessary. -/
+/-- Proposition 9.4.7 / Exercise 9.4.1.  It is possible that the hypothesis {lean}`x₀ ∈ X` is unnecessary. -/
 theorem ContinuousWithinAt.tfae (X:Set ℝ) (f: ℝ → ℝ) {x₀:ℝ} (h : x₀ ∈ X) :
   [
     ContinuousWithinAt f X x₀,
diff --git a/analysis/Analysis/Section_9_5.lean b/Analysis/Section_9_5.lean
similarity index 100%
rename from analysis/Analysis/Section_9_5.lean
rename to Analysis/Section_9_5.lean
diff --git a/analysis/Analysis/Section_9_6.lean b/Analysis/Section_9_6.lean
similarity index 100%
rename from analysis/Analysis/Section_9_6.lean
rename to Analysis/Section_9_6.lean
diff --git a/analysis/Analysis/Section_9_7.lean b/Analysis/Section_9_7.lean
similarity index 97%
rename from analysis/Analysis/Section_9_7.lean
rename to Analysis/Section_9_7.lean
index 5c9384e3..b671a9e1 100644
--- a/analysis/Analysis/Section_9_7.lean
+++ b/Analysis/Section_9_7.lean
@@ -36,7 +36,7 @@ theorem intermediate_value {a b:ℝ} (hab: a < b) {f:ℝ → ℝ} (hf: Continuou
     set c := sSup E
     have hc : c ∈ Set.Icc a b := by
       simp; split_ands
-      . solve_by_elim [ConditionallyCompleteLattice.le_csSup]
+      . solve_by_elim [le_csSup]
       convert csSup_le_csSup bddAbove_Icc hE_nonempty hE
       grind [csSup_Icc]
     use c, hc
@@ -53,7 +53,7 @@ theorem intermediate_value {a b:ℝ} (hab: a < b) {f:ℝ → ℝ} (hf: Continuou
         . convert tendsto_one_div_add_atTop_nhds_zero_nat.const_sub c;simp
         . exact tendsto_const_nhds
         . exact fun n ↦ le_of_lt (hx2 n)
-        exact fun n ↦ ConditionallyCompleteLattice.le_csSup _ _ hE_bdd (hx1 n)
+        exact fun n ↦ le_csSup hE_bdd (hx1 n)
       replace := this.comp_of_continuous hc (hf.continuousWithinAt hc) (fun n ↦ hE (hx1 n))
       have hfxny (n:ℕ) : f (x n) ≤ y := by specialize hx1 n; simp [E] at hx1; grind
       exact le_of_tendsto' this hfxny
diff --git a/analysis/Analysis/Section_9_8.lean b/Analysis/Section_9_8.lean
similarity index 100%
rename from analysis/Analysis/Section_9_8.lean
rename to Analysis/Section_9_8.lean
diff --git a/analysis/Analysis/Section_9_9.lean b/Analysis/Section_9_9.lean
similarity index 98%
rename from analysis/Analysis/Section_9_9.lean
rename to Analysis/Section_9_9.lean
index 6e960485..368ecb4a 100644
--- a/analysis/Analysis/Section_9_9.lean
+++ b/Analysis/Section_9_9.lean
@@ -2,7 +2,6 @@ import Mathlib.Tactic
 import Analysis.Section_6_1
 import Mathlib.Data.Nat.Nth
 import Analysis.Section_9_6
-
 /-!
 # Analysis I, Section 9.9: Uniform continuity
 
@@ -13,7 +12,7 @@ the Lean code could be "golfed" to be more elegant and idiomatic, but I have con
 doing so.
 
 Main constructions and results of this section:
-- API for Mathlib's `UniformContinuousOn`.
+- API for Mathlib's {name}`UniformContinuousOn`.
 - Continuous functions on compact intervals are uniformly continuous.
 
 -/
@@ -64,7 +63,7 @@ example (x₀ x : ℝ) :
   extract_lets g ε δ
   sorry
 
-/-- Definition 9.9.2.  Here we use the Mathlib term `UniformContinuousOn` -/
+/-- Definition 9.9.2.  Here we use the Mathlib term {name}`UniformContinuousOn` -/
 theorem UniformContinuousOn.iff (f: ℝ → ℝ) (X:Set ℝ) : UniformContinuousOn f X  ↔
   ∀ ε > (0:ℝ), ∃ δ > (0:ℝ), ∀ x₀ ∈ X, ∀ x ∈ X, δ.Close x x₀ → ε.Close (f x) (f x₀) := by
   simp_rw [Metric.uniformContinuousOn_iff_le, Real.Close]
diff --git a/analysis/Analysis/Tools/ExistsUnique.lean b/Analysis/Tools/ExistsUnique.lean
similarity index 86%
rename from analysis/Analysis/Tools/ExistsUnique.lean
rename to Analysis/Tools/ExistsUnique.lean
index 8d517727..de816825 100644
--- a/analysis/Analysis/Tools/ExistsUnique.lean
+++ b/Analysis/Tools/ExistsUnique.lean
@@ -3,7 +3,7 @@ import Mathlib.Tactic
 /-!
 # API for ExistsUnique
 
-Here we review some of the API provided for `ExistsUnique` in Mathlib, and provide some additional tools.  (Some of these might be suitable for upstreaming to Mathlib.)
+Here we review some of the API provided for {name}`ExistsUnique` in Mathlib, and provide some additional tools.  (Some of these might be suitable for upstreaming to Mathlib.)
 
 -/
 
@@ -35,7 +35,7 @@ noncomputable def Subsingleton.choose {α: Sort*} [Subsingleton α] [hn: Nonempt
 
 theorem Subsingleton.choose_spec {α: Sort*} [hs: Subsingleton α] [Nonempty α] (x:α) : x = hs.choose := Subsingleton.elim _ _
 
-/-- The equivalence between `ExistsUnique` and `[Subsingleton] [Nonempty]` does not require choice. -/
+/-- The equivalence between {name}`ExistsUnique` and {name}`Subsingleton`/{name}`Nonempty` does not require choice. -/
 theorem ExistsUnique.iff_subsingleton_nonempty  {α: Sort*} {p: α → Prop} :
   (∃! x, p x) ↔ (Subsingleton {x // p x} ∧ Nonempty {x // p x}) := by
   constructor
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 9a7f75e3..232eaa74 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -1,12 +1,9 @@
 # Contributing
 
-I would be interested in having volunteers “playtest” the companion to see if this can actually be done (and if the helper lemmas or “API” provided in the Lean files are sufficient to fill in the sorries in a conceptually straightforward manner without having to rely on more esoteric Lean programming techniques). Any other feedback will of course also be welcome.
+I would be interested in having volunteers "playtest" the companion to see if this can actually be done (and if the helper lemmas or "API" provided in the Lean files are sufficient to fill in the sorries in a conceptually straightforward manner without having to rely on more esoteric Lean programming techniques). Any other feedback will of course also be welcome.
 
 
 # Adding a section
 
-1. Add the relevant file to `analysis/Analysis`
-2. Copy a line of the `sections` definition in `book/lakefile.lean`, adapt it to the new section.
-3. Add a line to the `demoSite` definition in `book/AnalysisBook.lean` for the new section.
-4. Adapt the line in the README
-5. Add a line in `book/AnalysisBook/Home.lean`
\ No newline at end of file
+1. Add the relevant file to `Analysis/`
+2. Adapt the line in the README
diff --git a/README.md b/README.md
index 1e19e3ce..8df1a651 100644
--- a/README.md
+++ b/README.md
@@ -18,109 +18,109 @@ In order to align the formalization with Mathlib conventions, a small number of
 
 - _Chapter 1: Introduction (not formalized)_
 - Chapter 2: Starting at the beginning: the natural numbers
-  - Section 2.1: The Peano axioms ([Verso page](https://teorth.github.io/analysis/sec21/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_2_1.lean))
-  - Section 2.2: Addition ([Verso page](https://teorth.github.io/analysis/sec22/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_2_2.lean))
-  - Section 2.3: Multiplication ([Verso page](https://teorth.github.io/analysis/sec23/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_2_3.lean))
-  - Chapter 2 epilogue: Isomorphism with the Mathlib natural numbers ([Verso page](https://teorth.github.io/analysis/sec2e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_2_epilogue.lean))
+  - Section 2.1: The Peano axioms ([Verso page](https://teorth.github.io/analysis/sec21/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_2_1.lean))
+  - Section 2.2: Addition ([Verso page](https://teorth.github.io/analysis/sec22/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_2_2.lean))
+  - Section 2.3: Multiplication ([Verso page](https://teorth.github.io/analysis/sec23/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_2_3.lean))
+  - Chapter 2 epilogue: Isomorphism with the Mathlib natural numbers ([Verso page](https://teorth.github.io/analysis/sec2e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_2_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_2_epilogue.lean))
 - Chapter 3: Set theory
-  - Section 3.1: Fundamentals ([Verso page](https://teorth.github.io/analysis/sec31/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_1.lean))
-  - Section 3.2: Russell's paradox ([Verso page](https://teorth.github.io/analysis/sec32/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_2.lean))
-  - Section 3.3: Functions ([Verso page](https://teorth.github.io/analysis/sec33/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_3.lean))
-  - Section 3.4: Images and inverse images ([Verso page](https://teorth.github.io/analysis/sec34/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_4.lean))
-  - Section 3.5: Cartesian products ([Verso page](https://teorth.github.io/analysis/sec35/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_5.lean))
-  - Section 3.6: Cardinality of sets ([Verso page](https://teorth.github.io/analysis/sec36/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_6.lean))
-  - Chapter 3 epilogue: Connections with ZFSet ([Verso page](https://teorth.github.io/analysis/sec3e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_3_epilogue.lean))
+  - Section 3.1: Fundamentals ([Verso page](https://teorth.github.io/analysis/sec31/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_1.lean))
+  - Section 3.2: Russell's paradox ([Verso page](https://teorth.github.io/analysis/sec32/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_2.lean))
+  - Section 3.3: Functions ([Verso page](https://teorth.github.io/analysis/sec33/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_3.lean))
+  - Section 3.4: Images and inverse images ([Verso page](https://teorth.github.io/analysis/sec34/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_4.lean))
+  - Section 3.5: Cartesian products ([Verso page](https://teorth.github.io/analysis/sec35/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_5.lean))
+  - Section 3.6: Cardinality of sets ([Verso page](https://teorth.github.io/analysis/sec36/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_6.lean))
+  - Chapter 3 epilogue: Connections with ZFSet ([Verso page](https://teorth.github.io/analysis/sec3e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_3_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_3_epilogue.lean))
 - Chapter 4: Integers and rationals
-  - Section 4.1: The integers ([Verso page](https://teorth.github.io/analysis/sec41/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_4_1.lean))
-  - Section 4.2: The rationals ([Verso page](https://teorth.github.io/analysis/sec42/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_4_2.lean))
-  - Section 4.3: Absolute value and exponentiation ([Verso page](https://teorth.github.io/analysis/sec43/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_4_3.lean))
-  - Section 4.4: Gaps in the rational numbers ([Verso page](https://teorth.github.io/analysis/sec44/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_4_4.lean))
+  - Section 4.1: The integers ([Verso page](https://teorth.github.io/analysis/sec41/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_4_1.lean))
+  - Section 4.2: The rationals ([Verso page](https://teorth.github.io/analysis/sec42/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_4_2.lean))
+  - Section 4.3: Absolute value and exponentiation ([Verso page](https://teorth.github.io/analysis/sec43/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_4_3.lean))
+  - Section 4.4: Gaps in the rational numbers ([Verso page](https://teorth.github.io/analysis/sec44/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_4_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_4_4.lean))
 - Chapter 5: The Real numbers
-  - Section 5.1: Cauchy sequences of rationals ([Verso page](https://teorth.github.io/analysis/sec51/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_1.lean))
-  - Section 5.2: Equivalent Cauchy sequences ([Verso page](https://teorth.github.io/analysis/sec52/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_2.lean))
-  - Section 5.3: Construction of the real numbers ([Verso page](https://teorth.github.io/analysis/sec53/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_3.lean))
-  - Section 5.4: Ordering the reals ([Verso page](https://teorth.github.io/analysis/sec54/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_4.lean))
-  - Section 5.5: The least upper bound property ([Verso page](https://teorth.github.io/analysis/sec55/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_5.lean))
-  - Section 5.6: Real exponentiation, part I ([Verso page](https://teorth.github.io/analysis/sec56/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_6.lean))
-  - Chapter 5 epilogue: Isomorphism with the Mathlib real numbers ([Verso page](https://teorth.github.io/analysis/sec5e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_5_epilogue.lean))
+  - Section 5.1: Cauchy sequences of rationals ([Verso page](https://teorth.github.io/analysis/sec51/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_1.lean))
+  - Section 5.2: Equivalent Cauchy sequences ([Verso page](https://teorth.github.io/analysis/sec52/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_2.lean))
+  - Section 5.3: Construction of the real numbers ([Verso page](https://teorth.github.io/analysis/sec53/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_3.lean))
+  - Section 5.4: Ordering the reals ([Verso page](https://teorth.github.io/analysis/sec54/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_4.lean))
+  - Section 5.5: The least upper bound property ([Verso page](https://teorth.github.io/analysis/sec55/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_5.lean))
+  - Section 5.6: Real exponentiation, part I ([Verso page](https://teorth.github.io/analysis/sec56/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_6.lean))
+  - Chapter 5 epilogue: Isomorphism with the Mathlib real numbers ([Verso page](https://teorth.github.io/analysis/sec5e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_5_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_5_epilogue.lean))
 - Chapter 6: Limits of sequences
-  - Section 6.1: Convergence and limit laws ([Verso page](https://teorth.github.io/analysis/sec61/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_1.lean))
-  - Section 6.2: The extended real number system ([Verso page](https://teorth.github.io/analysis/sec62/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_2.lean))
-  - Section 6.3: Suprema and Infima of sequences ([Verso page](https://teorth.github.io/analysis/sec63/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_3.lean))
-  - Section 6.4: Limsup, Liminf, and limit points ([Verso page](https://teorth.github.io/analysis/sec64/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_4.lean))
-  - Section 6.5: Some standard limits ([Verso page](https://teorth.github.io/analysis/sec65/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_5.lean))
-  - Section 6.6: Subsequences ([Verso page](https://teorth.github.io/analysis/sec66/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_6.lean))
-  - Section 6.7: Real exponentiation, part II ([Verso page](https://teorth.github.io/analysis/sec67/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_7.lean))
-  - Chapter 6 epilogue: Connections with Mathlib limits ([Verso page](https://teorth.github.io/analysis/sec6e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_6_epilogue.lean))
+  - Section 6.1: Convergence and limit laws ([Verso page](https://teorth.github.io/analysis/sec61/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_1.lean))
+  - Section 6.2: The extended real number system ([Verso page](https://teorth.github.io/analysis/sec62/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_2.lean))
+  - Section 6.3: Suprema and Infima of sequences ([Verso page](https://teorth.github.io/analysis/sec63/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_3.lean))
+  - Section 6.4: Limsup, Liminf, and limit points ([Verso page](https://teorth.github.io/analysis/sec64/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_4.lean))
+  - Section 6.5: Some standard limits ([Verso page](https://teorth.github.io/analysis/sec65/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_5.lean))
+  - Section 6.6: Subsequences ([Verso page](https://teorth.github.io/analysis/sec66/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_6.lean))
+  - Section 6.7: Real exponentiation, part II ([Verso page](https://teorth.github.io/analysis/sec67/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_7.lean))
+  - Chapter 6 epilogue: Connections with Mathlib limits ([Verso page](https://teorth.github.io/analysis/sec6e/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_6_epilogue.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_6_epilogue.lean))
 - Chapter 7: Series
-  - Section 7.1: Finite series ([Verso page](https://teorth.github.io/analysis/sec71/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_7_1.lean))
-  - Section 7.2: Infinite series ([Verso page](https://teorth.github.io/analysis/sec72/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_7_2.lean))
-  - Section 7.3: Sums of non-negative numbers ([Verso page](https://teorth.github.io/analysis/sec73/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_7_3.lean))
-  - Section 7.4: Rearrangement of series ([Verso page](https://teorth.github.io/analysis/sec74/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_7_4.lean))
-  - Section 7.5: The root and ratio tests ([Verso page](https://teorth.github.io/analysis/sec75/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_7_5.lean))
+  - Section 7.1: Finite series ([Verso page](https://teorth.github.io/analysis/sec71/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_7_1.lean))
+  - Section 7.2: Infinite series ([Verso page](https://teorth.github.io/analysis/sec72/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_7_2.lean))
+  - Section 7.3: Sums of non-negative numbers ([Verso page](https://teorth.github.io/analysis/sec73/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_7_3.lean))
+  - Section 7.4: Rearrangement of series ([Verso page](https://teorth.github.io/analysis/sec74/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_7_4.lean))
+  - Section 7.5: The root and ratio tests ([Verso page](https://teorth.github.io/analysis/sec75/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_7_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_7_5.lean))
 - Chapter 8: Infinite sets
-  - Section 8.1: Countability ([Verso page](https://teorth.github.io/analysis/sec81/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_8_1.lean))
-  - Section 8.2: Summation on infinite sets ([Verso page](https://teorth.github.io/analysis/sec82/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_8_2.lean))
-  - Section 8.3: Uncountable sets ([Verso page](https://teorth.github.io/analysis/sec83/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_8_3.lean))
-  - Section 8.4: The axiom of choice ([Verso page](https://teorth.github.io/analysis/sec84/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_8_4.lean))
-  - Section 8.5: Ordered sets ([Verso page](https://teorth.github.io/analysis/sec85/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_8_5.lean))
+  - Section 8.1: Countability ([Verso page](https://teorth.github.io/analysis/sec81/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_8_1.lean))
+  - Section 8.2: Summation on infinite sets ([Verso page](https://teorth.github.io/analysis/sec82/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_8_2.lean))
+  - Section 8.3: Uncountable sets ([Verso page](https://teorth.github.io/analysis/sec83/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_8_3.lean))
+  - Section 8.4: The axiom of choice ([Verso page](https://teorth.github.io/analysis/sec84/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_8_4.lean))
+  - Section 8.5: Ordered sets ([Verso page](https://teorth.github.io/analysis/sec85/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_8_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_8_5.lean))
 - Chapter 9: Continuous functions on `ℝ`
-  - Section 9.1: Subsets of the real line ([Verso page](https://teorth.github.io/analysis/sec91/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_1.lean))
-  - Section 9.2: The algebra of real-valued functions ([Verso page](https://teorth.github.io/analysis/sec92/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_2.lean))
-  - Section 9.3: Limiting values of functions ([Verso page](https://teorth.github.io/analysis/sec93/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_3.lean))
-  - Section 9.4: Continuous functions ([Verso page](https://teorth.github.io/analysis/sec94/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_4.lean))
-  - Section 9.5: Left and right limits ([Verso page](https://teorth.github.io/analysis/sec95/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_5.lean))
-  - Section 9.6: The maximum principle ([Verso page](https://teorth.github.io/analysis/sec96/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_6.lean))
-  - Section 9.7: The intermediate value theorem ([Verso page](https://teorth.github.io/analysis/sec97/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_7.lean))
-  - Section 9.8: Monotonic functions ([Verso page](https://teorth.github.io/analysis/sec98/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_8.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_8.lean))
-  - Section 9.9: Uniform continuity ([Verso page](https://teorth.github.io/analysis/sec99/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_9.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_9.lean))
-  - Section 9.10: Limits at infinity ([Verso page](https://teorth.github.io/analysis/sec910/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_10.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_9_10.lean))
+  - Section 9.1: Subsets of the real line ([Verso page](https://teorth.github.io/analysis/sec91/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_1.lean))
+  - Section 9.2: The algebra of real-valued functions ([Verso page](https://teorth.github.io/analysis/sec92/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_2.lean))
+  - Section 9.3: Limiting values of functions ([Verso page](https://teorth.github.io/analysis/sec93/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_3.lean))
+  - Section 9.4: Continuous functions ([Verso page](https://teorth.github.io/analysis/sec94/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_4.lean))
+  - Section 9.5: Left and right limits ([Verso page](https://teorth.github.io/analysis/sec95/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_5.lean))
+  - Section 9.6: The maximum principle ([Verso page](https://teorth.github.io/analysis/sec96/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_6.lean))
+  - Section 9.7: The intermediate value theorem ([Verso page](https://teorth.github.io/analysis/sec97/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_7.lean))
+  - Section 9.8: Monotonic functions ([Verso page](https://teorth.github.io/analysis/sec98/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_8.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_8.lean))
+  - Section 9.9: Uniform continuity ([Verso page](https://teorth.github.io/analysis/sec99/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_9.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_9.lean))
+  - Section 9.10: Limits at infinity ([Verso page](https://teorth.github.io/analysis/sec910/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_9_10.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_9_10.lean))
 - Chapter 10: Differentiation of functions
-  - Section 10.1: Basic definitions ([Verso page](https://teorth.github.io/analysis/sec101/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_10_1.lean))
-  - Section 10.2: Local maxima, local minima, and derivatives ([Verso page](https://teorth.github.io/analysis/sec102/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_10_2.lean))
-  - Section 10.3: Monotone functions and derivatives ([Verso page](https://teorth.github.io/analysis/sec103/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_10_3.lean))
-  - Section 10.4: Inverse functions and derivatives ([Verso page](https://teorth.github.io/analysis/sec104/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_10_4.lean))
-  - Section 10.5: L'Hôpital's rule ([Verso page](https://teorth.github.io/analysis/sec105/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_10_5.lean))
+  - Section 10.1: Basic definitions ([Verso page](https://teorth.github.io/analysis/sec101/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_10_1.lean))
+  - Section 10.2: Local maxima, local minima, and derivatives ([Verso page](https://teorth.github.io/analysis/sec102/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_10_2.lean))
+  - Section 10.3: Monotone functions and derivatives ([Verso page](https://teorth.github.io/analysis/sec103/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_10_3.lean))
+  - Section 10.4: Inverse functions and derivatives ([Verso page](https://teorth.github.io/analysis/sec104/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_10_4.lean))
+  - Section 10.5: L'Hôpital's rule ([Verso page](https://teorth.github.io/analysis/sec105/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_10_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_10_5.lean))
 - Chapter 11: The Riemann integral
-  - Section 11.1: Partitions ([Verso page](https://teorth.github.io/analysis/sec111/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_1.lean))
-  - Section 11.2: Piecewise constant functions ([Verso page](https://teorth.github.io/analysis/sec112/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_2.lean))
-  - Section 11.3: Upper and lower Riemann integrals ([Verso page](https://teorth.github.io/analysis/sec113/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_3.lean))
-  - Section 11.4: Basic properties of the Riemann integral ([Verso page](https://teorth.github.io/analysis/sec114/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_4.lean))
-  - Section 11.5: Riemann integrability of continuous functions ([Verso page](https://teorth.github.io/analysis/sec115/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_5.lean))
-  - Section 11.6: Riemann integrability of monotone functions ([Verso page](https://teorth.github.io/analysis/sec116/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_6.lean))
-  - Section 11.7: A non-Riemann integrable function ([Verso page](https://teorth.github.io/analysis/sec117/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_7.lean))
-  - Section 11.8: The Riemann-Stieltjes integral ([Verso page](https://teorth.github.io/analysis/sec118/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_8.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_8.lean))
-  - Section 11.9: The two fundamental theorems of calculus ([Verso page](https://teorth.github.io/analysis/sec119/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_9.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_9.lean))
-  - Section 11.10: Consequences of the fundamental theorem of calculus ([Verso page](https://teorth.github.io/analysis/sec1110/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_10.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Section_11_10.lean))
+  - Section 11.1: Partitions ([Verso page](https://teorth.github.io/analysis/sec111/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_1.lean))
+  - Section 11.2: Piecewise constant functions ([Verso page](https://teorth.github.io/analysis/sec112/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_2.lean))
+  - Section 11.3: Upper and lower Riemann integrals ([Verso page](https://teorth.github.io/analysis/sec113/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_3.lean))
+  - Section 11.4: Basic properties of the Riemann integral ([Verso page](https://teorth.github.io/analysis/sec114/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_4.lean))
+  - Section 11.5: Riemann integrability of continuous functions ([Verso page](https://teorth.github.io/analysis/sec115/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_5.lean))
+  - Section 11.6: Riemann integrability of monotone functions ([Verso page](https://teorth.github.io/analysis/sec116/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_6.lean))
+  - Section 11.7: A non-Riemann integrable function ([Verso page](https://teorth.github.io/analysis/sec117/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_7.lean))
+  - Section 11.8: The Riemann-Stieltjes integral ([Verso page](https://teorth.github.io/analysis/sec118/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_8.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_8.lean))
+  - Section 11.9: The two fundamental theorems of calculus ([Verso page](https://teorth.github.io/analysis/sec119/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_9.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_9.lean))
+  - Section 11.10: Consequences of the fundamental theorem of calculus ([Verso page](https://teorth.github.io/analysis/sec1110/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Section_11_10.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Section_11_10.lean))
 - Appendix A: The basics of mathematical logic
-  - A.1: Mathematical statements ([Verso page](https://teorth.github.io/analysis/appA1/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_1.lean))
-  - A.2: Implication ([Verso page](https://teorth.github.io/analysis/appA2/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_2.lean))
-  - A.3: The structure of proofs ([Verso page](https://teorth.github.io/analysis/appA3/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_3.lean))
-  - A.4: Variables and quantifiers ([Verso page](https://teorth.github.io/analysis/appA4/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_4.lean))
-  - A.5: Nested quantifiers ([Verso page](https://teorth.github.io/analysis/appA5/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_5.lean))
-  - A.6: Some examples of proofs and quantifiers ([Verso page](https://teorth.github.io/analysis/appA6/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_6.lean))
-  - A.7: Equality ([Verso page](https://teorth.github.io/analysis/appA7/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_A_7.lean))
+  - A.1: Mathematical statements ([Verso page](https://teorth.github.io/analysis/appA1/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_1.lean))
+  - A.2: Implication ([Verso page](https://teorth.github.io/analysis/appA2/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_2.lean))
+  - A.3: The structure of proofs ([Verso page](https://teorth.github.io/analysis/appA3/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_3.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_3.lean))
+  - A.4: Variables and quantifiers ([Verso page](https://teorth.github.io/analysis/appA4/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_4.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_4.lean))
+  - A.5: Nested quantifiers ([Verso page](https://teorth.github.io/analysis/appA5/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_5.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_5.lean))
+  - A.6: Some examples of proofs and quantifiers ([Verso page](https://teorth.github.io/analysis/appA6/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_6.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_6.lean))
+  - A.7: Equality ([Verso page](https://teorth.github.io/analysis/appA7/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_A_7.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_A_7.lean))
 - Appendix B: The decimal system
-  - B.1: The decimal representation of natural numbers ([Verso page](https://teorth.github.io/analysis/appB1/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_B_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_B_1.lean))
-  - B.2: The decimal representation of real numbers ([Verso page](https://teorth.github.io/analysis/appB2/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_B_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Appendix_B_2.lean))
+  - B.1: The decimal representation of natural numbers ([Verso page](https://teorth.github.io/analysis/appB1/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_B_1.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_B_1.lean))
+  - B.2: The decimal representation of real numbers ([Verso page](https://teorth.github.io/analysis/appB2/)) ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Appendix_B_2.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Appendix_B_2.lean))
 
 ## Additional content
 
 I am using this repository to host some other minor Lean content unrelated to the text book:
 
-- [A formalization of my book on Measure Theory](https://github.com/teorth/analysis/tree/main/analysis/Analysis/MeasureTheory) (work in progress)
+- [A formalization of my book on Measure Theory](https://github.com/teorth/analysis/tree/main/Analysis/MeasureTheory) (work in progress)
 - A formalization of physical units
-  - Support for systems of units ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/UnitsSystem.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/UnitsSystem.lean))
-    - Examples of use ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/UnitsSystemExamples.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/UnitsSystemExamples.lean))
-  - The SI system of units ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/SI.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/SI.lean))
-    - Examples of use ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/SIExamples.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/SIExamples.lean))
+  - Support for systems of units ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/UnitsSystem.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/UnitsSystem.lean))
+    - Examples of use ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/UnitsSystemExamples.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/UnitsSystemExamples.lean))
+  - The SI system of units ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/SI.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/SI.lean))
+    - Examples of use ([Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/SIExamples.html)) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/SIExamples.lean))
 - A formalization of finite choice avoiding Lean's axiom of choice
-  - [Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/FiniteChoice.html) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/FiniteChoice.lean))
-- Some finite probability theory [Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/Probability.html) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/Probability.lean))
-- A [solution to Erdos problem \#379](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_379.html) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/erdos_379.lean))
-- [Pikhurko's counterexample to Erdos problem \#613](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_613.html) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/erdos_613.lean))
-- A [solution to Erdos problem \#707](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_707.html) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/erdos_707.lean))
-- A [solution to Erdos problem \#987](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_987.html) ([Lean source](https://github.com/teorth/analysis/blob/main/analysis/Analysis/Misc/erdos_987.lean))
+  - [Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/FiniteChoice.html) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/FiniteChoice.lean))
+- Some finite probability theory [Documentation](https://teorth.github.io/analysis/docs/Analysis/Misc/Probability.html) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/Probability.lean))
+- A [solution to Erdos problem \#379](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_379.html) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/erdos_379.lean))
+- [Pikhurko's counterexample to Erdos problem \#613](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_613.html) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/erdos_613.lean))
+- A [solution to Erdos problem \#707](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_707.html) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/erdos_707.lean))
+- A [solution to Erdos problem \#987](https://teorth.github.io/analysis/docs/Analysis/Misc/erdos_987.html) ([Lean source](https://github.com/teorth/analysis/blob/main/Analysis/Misc/erdos_987.lean))
 
 ## Other resources
 
@@ -179,20 +179,17 @@ To build the project's web page after [installing Lean](https://lean-lang.org/do
 % ./build-web.sh
 ```
 
-After this, `book/_site/` contains the project's web page.
+After this, `_site/` contains the project's web page.
 This can be served as a webpage by executing `python3 serve.py`
 
 ### Updating the Lean/Mathlib version
 
 Because this project uses a deprecated method to conditionally require `doc-gen4`
 in order to update the version of Lean and Mathlib used in the project you need to:
-* edit the `analysis/lakefile.lean` to change the `require` lines for Mathlib and doc-gen4,
+* edit the `lakefile.lean` to change the `require` lines for Mathlib and doc-gen4,
   to pin to the tag corresponding to the next Lean version
   (it is highly recommended that you update in incremental steps)
-* edit the `analysis/lean-toolchain` to change the Lean version to the next version
-* in `analysis/`, run `lake update -R -Kenv=dev`
+* edit the `lean-toolchain` to change the Lean version to the next version
+* run `lake update -R -Kenv=dev`
 * this may have the side effect of setting your `lean-toolchain` to the *latest* Lean version;
   if so, revert it to the intended version
-
-It is essential that the dependencies on `subverso` in the `analysis/` and `book/` directories
-stay in sync (in particular, matching the toolchain used in the `book/` directory).
diff --git a/analysis/LiterateExtract.lean b/analysis/LiterateExtract.lean
deleted file mode 100644
index 596f1fc7..00000000
--- a/analysis/LiterateExtract.lean
+++ /dev/null
@@ -1,230 +0,0 @@
-/-
-Copyright (c) 2023-2024 Lean FRO LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Author: David Thrane Christiansen
--/
-import SubVerso.Compat
-import SubVerso.Examples.Env
-import SubVerso.Module
-import MD4Lean
-
-open Lean Elab Frontend
-open Lean.Elab.Command hiding Context
-open SubVerso Examples Module
-open SubVerso.Highlighting (Highlighted highlight highlightMany highlightFrontendResult)
-
-def helpText : String :=
-"Extract a module's highlighted representation as JSON
-
-Usage: subverso-extract-mod [OPTS] MOD [OUT]
-
-MOD is the name of a Lean module, and OUT is the destination of the JSON.
-If OUT is not specified, the JSON is emitted to standard output.
-
-OPTS may be:
-  --suppress-namespace NS
-    Suppress the showing of namespace NS in metadata
-
-  --suppress-namespaces FILE
-    Suppress the showing of the whitespace-delimited list of namespaces in FILE
-
-Each command in the module is represented as a JSON object with the following
-fields:
-
- * \"kind\": the syntax kind of the command, as emitted by the Lean parser
-
- * \"range\": the start and end source positions of the command. Line and column
-   numbers are one-based, so the start of the file is {\"line\": 1, \"column\": 1},
-   and columns are in terms of Unicode code points.
-
- * \"defines\": the names defined in the command, as an array of strings.
-
- * \"terms\": terms that occur as literals in documentation comments in the command,
-   as an object that maps the occurring strings to their highlighted representations.
-
- * \"code\": the JSON serialization of SubVerso's highlighted code datatype. The
-   specifics of this representation are an implementation detail, and it should
-   be deserialized using the same version of SubVerso.
-"
-
-partial def allCode (md : String) : StateM (Array String) Unit := do
-  MD4Lean.parse md |>.forM fun ⟨blocks⟩ => blocks.forM blockCode
-
-where
-  blockCode : MD4Lean.Block → StateM (Array String) Unit
-    | .p txts => txts.forM textCode
-    | .table xs ys => xs.forM (·.forM textCode) *> ys.forM (·.forM (·.forM textCode))
-    | .blockquote bs => bs.forM blockCode
-    | .code _ _ _ xs => modify (·.push <| "\n".intercalate xs.toList)
-    | .ul _ _ items | .ol _ _ _ items =>
-      items.forM fun i => i.contents.forM blockCode
-    | .header _ txt => txt.forM textCode
-    | .html .. | .hr => pure ()
-  textCode : MD4Lean.Text → StateM (Array String) Unit
-    | .code s => modify (·.push <| "\n".intercalate s.toList)
-    | .a _ _ _ xs | .wikiLink _ xs | .del xs | .u xs | .em xs | .strong xs | .img _ _ xs => xs.forM textCode
-    | .normal .. | .latexMathDisplay .. | .latexMath .. | .entity .. | .br .. | .softbr .. | .nullchar => pure ()
-
-
-open Lean.Parser.Command in
-def allTerms (stx : Syntax) : Array String := go stx |>.run #[] |>.snd
-where
-  go (stx : Syntax) : StateM (Array String) Unit :=
-    discard <| stx.replaceM fun s => do
-      if s.getKind == ``docComment || s.getKind == ``moduleDoc then
-        s[1].getAtomVal |> allCode
-        pure none
-      else
-        pure none
-
-/--
-Extends the last token's trailing whitespace to include the rest of the file.
--/
-partial def wholeFile (contents : String) (stx : Syntax) : Syntax :=
-  wholeFile' stx |>.getD stx
-where
-  wholeFile' : Syntax → Option Syntax
-  | Syntax.atom info val => pure <| Syntax.atom (wholeFileInfo info) val
-  | Syntax.ident info rawVal val pre => pure <| Syntax.ident (wholeFileInfo info) rawVal val pre
-  | Syntax.node info k args => do
-    for i in [0:args.size - 1] do
-      let j := args.size - (i + 1)
-      if let some s := wholeFile' args[j]! then
-        let args := args.set! j s
-        return Syntax.node info k args
-    none
-  | .missing => none
-
-  wholeFileInfo : SourceInfo → SourceInfo
-    | .original l l' t _ => .original l l' t contents.rawEndPos
-    | i => i
-
-structure ModuleItem' extends ModuleItem where
-  terms : Array (String × Highlighted)
-
-instance : ToJson ModuleItem' where
-  toJson v := toJson v.toModuleItem |>.setObjVal! "terms" (mkJson v.terms)
-where
-  mkJson xs := Json.mkObj <| xs.toList.map fun (txt, tm) => (txt, toJson tm)
-
-unsafe def go (suppressedNamespaces : Array Name) (mod : String) (out : IO.FS.Stream) : IO UInt32 := do
-  try
-    initSearchPath (← findSysroot)
-    let modName := mod.toName
-
-    let sp ← Compat.initSrcSearchPath
-    let sp : SearchPath := (sp : List System.FilePath) ++ [("." : System.FilePath)]
-    let fname ← do
-      if let some fname ← sp.findModuleWithExt "lean" modName then
-        pure fname
-      else
-        throw <| IO.userError s!"Failed to load {modName} from {sp}"
-    let contents ← IO.FS.readFile fname
-    let fm := FileMap.ofString contents
-    let ictx := Parser.mkInputContext contents fname.toString
-    let (headerStx, parserState, msgs) ← Parser.parseHeader ictx
-    let imports := headerToImports headerStx
-    enableInitializersExecution
-    let env ← Compat.importModules imports {}
-    let pctx : Context := {inputCtx := ictx}
-
-    let scopes := [{header := "", opts := maxHeartbeats.set {} 10000000 }]
-    let commandState := { env, maxRecDepth := defaultMaxRecDepth, messages := msgs, scopes }
-    let cmdPos := parserState.pos
-    let cmdSt ← IO.mkRef {commandState, parserState, cmdPos}
-
-    let res ← Compat.Frontend.processCommands headerStx pctx cmdSt
-
-    let msgs := Array.flatten (res.items.map (Compat.messageLogArray ·.messages))
-
-    let res := res.updateLeading contents
-
-    let hls ← (Frontend.runCommandElabM <| liftTermElabM <| highlightFrontendResult res (suppressNamespaces := suppressedNamespaces.toList)) pctx cmdSt
-
-    let env := (← cmdSt.get).commandState.env
-    let cmds := res.syntax
-    let getTerms := cmds.mapM fun (stx : Syntax) => show FrontendM _ from do
-      runCommandElabM <| elabCommand stx
-      let tms := allTerms stx
-      tms.mapM fun tm => show FrontendM _ from do
-        let .ok e := Parser.runParserCategory env `term tm
-          | pure (tm, Highlighted.empty)
-        let hl ← runCommandElabM <| withoutModifyingEnv <| Compat.commandWithoutAsync do
-          let infoState ← getInfoState
-          let messageLog ← modifyGet fun x => (x.messages, {x with messages := {}})
-          try
-            setInfoState {}
-            withEnableInfoTree true do
-              let cmd ← `(#check $(⟨e⟩))
-              try
-                elabCommand cmd
-              catch
-                | e =>
-                  dbg_trace (← e.toMessageData.toString)
-                  pure ()
-              let trees := (← get).infoState.trees
-              let msgs := (← get).messages
-              liftTermElabM <| do
-                highlight e msgs.toArray trees
-          finally
-            setInfoState infoState
-            modify fun x => {x with messages := messageLog}
-        pure (tm, hl)
-    let terms ← getTerms pctx cmdSt
-    let items : Array ModuleItem' := hls.zip (cmds |>.zip terms) |>.map fun (hl, stx, terms) => {
-      defines := hl.definedNames.toArray,
-      kind := stx.getKind,
-      range := stx.getRange?.map fun ⟨s, e⟩ => (fm.toPosition s, fm.toPosition e),
-      code := hl,
-      terms := terms
-    }
-
-    out.putStrLn (toString (Json.arr (items.map toJson)))
-
-    return (0 : UInt32)
-
-  catch e =>
-    IO.eprintln s!"error finding highlighted code: {toString e}"
-    return 2
-
-structure Config where
-  suppressedNamespaces : Array Name := #[]
-  mod : String
-  outFile : Option String := none
-
-private def readNamespaces (file : String) : IO (Array Name) := do
-  let contents ← IO.FS.readFile file
-  return contents.split (·.isWhitespace) |>.filter (!·.isEmpty) |>.map (·.toName) |>.toArray
-
-def Config.fromArgs (args : List String) : IO Config := go #[] args
-where
-  go (nss : Array Name) : List String → IO Config
-    | "--suppress-namespace" :: more =>
-      if let ns :: more := more then
-        go (nss.push ns.toName) more
-      else
-        throw <| IO.userError "No namespace given after --suppress-namespace"
-    | "--suppress-namespaces" :: file :: more' => do
-        let nss' ← readNamespaces file
-        go (nss ++ nss') more'
-    | "--suppress-namespaces" :: [] =>
-        throw <| IO.userError "No namespace file given after --suppress-namespaces"
-    | [mod] => pure {suppressedNamespaces := nss, mod}
-    | [mod, outFile] => pure {suppressedNamespaces := nss, mod, outFile := some outFile}
-    | other => throw <| IO.userError s!"Didn't understand remaining arguments: {other}"
-
-unsafe def main (args : List String) : IO UInt32 := do
-  try
-    let {suppressedNamespaces, mod, outFile} ← Config.fromArgs args
-    match outFile with
-    | none =>
-      go suppressedNamespaces mod (← IO.getStdout)
-    | some outFile =>
-      if let some p := (outFile : System.FilePath).parent then
-        IO.FS.createDirAll p
-      IO.FS.withFile outFile .write fun h =>
-        go suppressedNamespaces mod (.ofHandle h)
-  catch e =>
-    IO.eprintln e
-    IO.println helpText
-    pure 1
diff --git a/analysis/lakefile.lean b/analysis/lakefile.lean
deleted file mode 100644
index 27891a55..00000000
--- a/analysis/lakefile.lean
+++ /dev/null
@@ -1,64 +0,0 @@
-import Lake
-open Lake DSL
-
-package «Analysis» where
-  -- Settings applied to both builds and interactive editing
-  leanOptions := #[
-    ⟨`pp.unicode.fun, true⟩ -- pretty-prints `fun a ↦ b`
-  ]
-  -- Settings applied only to command line builds
-  moreLeanArgs := #[
-    "-Dwarn.sorry=false" -- suppress warnings about `sorry` on the command line; remove when project is complete
-  ]
-  -- add any additional package configuration options here
-
--- This library is needed to build the online version.
--- If ../book/lakefile.lean requires verso @ "v4.X.Y", then this line should require
--- subverso @ "verso-v4.X.Y".
--- Right now, it's set to `main` instead to get newer improvements; next time Verso is
--- updated in `../book/`, this should be set to the corresponding tag again.
-require subverso from git "https://github.com/leanprover/subverso" @ "main"
-
--- This library is needed to build the online version.
-require MD4Lean from git "https://github.com/acmepjz/md4lean" @ "main"
-
-meta if get_config? env = some "dev" then
-require «doc-gen4» from git "https://github.com/leanprover/doc-gen4" @ "main"
-
--- Require Mathlib (the comprehensive library of mathematics in Lean)
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git" @ "v4.29.0-rc6"
-
-
-@[default_target]
-lean_lib «Analysis» where
-  -- add any library configuration options here
-
-lean_exe "literate-extract" where
-  root := `LiterateExtract
-  supportInterpreter := true
-
-module_facet literate mod : System.FilePath := do
-  let ws ← getWorkspace
-
-  let exeJob ← «literate-extract».fetch
-  let modJob ← mod.olean.fetch
-
-  let buildDir := ws.root.buildDir
-  let hlFile := mod.filePath (buildDir / "literate") "json"
-
-  exeJob.bindM fun exeFile =>
-    modJob.mapM fun _oleanPath => do
-      buildFileUnlessUpToDate' (text := true) hlFile <|
-        proc {
-          cmd := exeFile.toString
-          args :=  #[mod.name.toString, hlFile.toString]
-          env := ← getAugmentedEnv
-        }
-      pure hlFile
-
-library_facet literate lib : Array System.FilePath := do
-  let mods ← (← lib.modules.fetch).await
-  let modJobs ← mods.mapM (·.facet `literate |>.fetch)
-  let out ← modJobs.mapM (·.await)
-  pure (.pure out)
diff --git a/analysis/lean-toolchain b/analysis/lean-toolchain
deleted file mode 100644
index 87b20aaf..00000000
--- a/analysis/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:v4.29.0-rc6
diff --git a/book/AnalysisBook.lean b/book/AnalysisBook.lean
deleted file mode 100644
index d4387321..00000000
--- a/book/AnalysisBook.lean
+++ /dev/null
@@ -1,132 +0,0 @@
-import VersoBlog
-import AnalysisBook.Home
-import AnalysisBook.LiterateModule
-import Book -- This imports the sections. It's generated by the `genLib` job in the Lake config
-
-
-open Verso Genre Blog Site Syntax
-
-open Output Html Template Theme in
-def theme : Theme := { Theme.default with
-  primaryTemplate := do
-    return {{
-      <html>
-        <head>
-          <meta charset="UTF-8"/>
-          <title>{{ (← param (α := String) "title") }} " — Verso "</title>
-          <base href="/analysis/"/>
-          <script>"window.__versoSiteRoot=\"/analysis/\""</script>
-          <link rel="stylesheet" href="static/style.css"/>
-          {{← builtinHeader }}
-        </head>
-        <body>
-          <header>
-            <div class="inner-wrap">
-
-            <nav class="top" role="navigation">
-              <ol>
-                <li><a href="/">"Home"</a></li>
-                <li><a href="/docs/">"Documentation"</a></li>
-                {{ ← dirLinks (← read).site }}
-              </ol>
-            </nav>
-          </div>
-          </header>
-          <div class="main" role="main">
-            <div class="wrap">
-              {{ (← param "content") }}
-            </div>
-          </div>
-        </body>
-      </html>
-    }}
-  }
-  |>.override #[] ⟨do return {{<div class="frontpage"><h1>{{← param "title"}}</h1> {{← param "content"}}</div>}}, id⟩
-
-
-def demoSite : Site := site AnalysisBook.Home /
-  static "static" ← "./static_files"
-  "sec21" Book.Analysis.Section_2_1
-  "sec22" Book.Analysis.Section_2_2
-  "sec23" Book.Analysis.Section_2_3
-  "sec2e" Book.Analysis.Section_2_epilogue
-  "sec31" Book.Analysis.Section_3_1
-  "sec32" Book.Analysis.Section_3_2
-  "sec33" Book.Analysis.Section_3_3
-  "sec34" Book.Analysis.Section_3_4
-  "sec35" Book.Analysis.Section_3_5
-  "sec36" Book.Analysis.Section_3_6
-  "sec3e" Book.Analysis.Section_3_epilogue
-  "sec41" Book.Analysis.Section_4_1
-  "sec42" Book.Analysis.Section_4_2
-  "sec43" Book.Analysis.Section_4_3
-  "sec44" Book.Analysis.Section_4_4
-  "sec51" Book.Analysis.Section_5_1
-  "sec52" Book.Analysis.Section_5_2
-  "sec53" Book.Analysis.Section_5_3
-  "sec54" Book.Analysis.Section_5_4
-  "sec55" Book.Analysis.Section_5_5
-  "sec56" Book.Analysis.Section_5_6
-  "sec5e" Book.Analysis.Section_5_epilogue
-  "sec61" Book.Analysis.Section_6_1
-  "sec62" Book.Analysis.Section_6_2
-  "sec63" Book.Analysis.Section_6_3
-  "sec64" Book.Analysis.Section_6_4
-  "sec65" Book.Analysis.Section_6_5
-  "sec66" Book.Analysis.Section_6_6
-  "sec67" Book.Analysis.Section_6_7
-  "sec6e" Book.Analysis.Section_6_epilogue
-  "sec71" Book.Analysis.Section_7_1
-  "sec72" Book.Analysis.Section_7_2
-  "sec73" Book.Analysis.Section_7_3
-  "sec74" Book.Analysis.Section_7_4
-  "sec75" Book.Analysis.Section_7_5
-  "sec81" Book.Analysis.Section_8_1
-  "sec82" Book.Analysis.Section_8_2
-  "sec83" Book.Analysis.Section_8_3
-  "sec84" Book.Analysis.Section_8_4
-  "sec85" Book.Analysis.Section_8_5
-  "sec91" Book.Analysis.Section_9_1
-  "sec92" Book.Analysis.Section_9_2
-  "sec93" Book.Analysis.Section_9_3
-  "sec94" Book.Analysis.Section_9_4
-  "sec95" Book.Analysis.Section_9_5
-  "sec96" Book.Analysis.Section_9_6
-  "sec97" Book.Analysis.Section_9_7
-  "sec98" Book.Analysis.Section_9_8
-  "sec99" Book.Analysis.Section_9_9
-  "sec910" Book.Analysis.Section_9_10
-  "sec101" Book.Analysis.Section_10_1
-  "sec102" Book.Analysis.Section_10_2
-  "sec103" Book.Analysis.Section_10_3
-  "sec104" Book.Analysis.Section_10_4
-  "sec105" Book.Analysis.Section_10_5
-  "sec111" Book.Analysis.Section_11_1
-  "sec112" Book.Analysis.Section_11_2
-  "sec113" Book.Analysis.Section_11_3
-  "sec114" Book.Analysis.Section_11_4
-  "sec115" Book.Analysis.Section_11_5
-  "sec116" Book.Analysis.Section_11_6
-  "sec117" Book.Analysis.Section_11_7
-  "sec118" Book.Analysis.Section_11_8
-  "sec119" Book.Analysis.Section_11_9
-  "sec1110" Book.Analysis.Section_11_10
-  "appA1" Book.Analysis.Appendix_A_1
-  "appA2" Book.Analysis.Appendix_A_2
-  "appA3" Book.Analysis.Appendix_A_3
-  "appA4" Book.Analysis.Appendix_A_4
-  "appA5" Book.Analysis.Appendix_A_5
-  "appA6" Book.Analysis.Appendix_A_6
-  "appA7" Book.Analysis.Appendix_A_7
-  "appB1" Book.Analysis.Appendix_B_1
-  "appB2" Book.Analysis.Appendix_B_2
-
-def baseUrl := "https://teorth.github.io/analysis/docs/"
-
-def linkTargets : Code.LinkTargets α where
-  const name _ := #[mkLink s!"{baseUrl}find?pattern={name}#doc"]
-  definition name _ := #[mkLink s!"{baseUrl}find?pattern={name}#doc"]
-where
-  mkLink href := {shortDescription := "doc", description := "API documentation", href}
-
-def main := blogMain theme demoSite (linkTargets := linkTargets)
diff --git a/book/AnalysisBook/Home.lean b/book/AnalysisBook/Home.lean
deleted file mode 100644
index b4158b92..00000000
--- a/book/AnalysisBook/Home.lean
+++ /dev/null
@@ -1,93 +0,0 @@
-import VersoBlog
-open Verso Genre Blog
-
-#doc (Page) " Partial Lean formalization of Analysis I" =>
-
-The files in this directory contain a formalization of selected portions of my text [_Analysis I_](https://terrytao.wordpress.com/books/analysis-i/) into [Lean](https://lean-lang.org/). The formalization is intended to be as faithful a paraphrasing as possible to the original text, while also showcasing Lean's features and syntax.  In particular, the formalization is _not_ optimized for efficiency, and in some cases may deviate from idiomatic Lean usage.
-
-Portions of the text that were left as exercises to the reader are rendered in this translation as `sorry`s.  Readers are welcome to fork the repository here to try their hand at these exercises, but I do not intend to place solutions in this repository directly.
-
-While the arrangement of definitions, theorems, and proofs here are closely paraphrasing the textbook, I am refraining from directly quoting material from the textbook, instead providing references to the original text where appropriate.  As such, this formalization should be viewed as an annotated companion to the primary text, rather than a replacement for it.
-
-Much of the material in this text is duplicated in Lean's standard math library [Mathlib](https://leanprover-community.github.io/mathlib4_docs/), though with slightly different definitions.  To reconcile these discrepancies, this formalization will gradually transition from the textbook-provided definitions to the Mathlib-provided definitions as one progresses further into the text, thus sacrificing the self-containedness of the formalization in favor of compatibility with Mathlib.  For instance, Chapter 2 develops a theory of the natural numbers independent of Mathlib, but all subsequent chapters will use the Mathlib natural numbers instead.  (An epilogue to Chapter 2 is provided to show that the two notions of the natural numbers are isomorphic.)  As such, this formalization can also be used as an introduction to various portions of Mathlib.
-
-In order to align the formalization with Mathlib conventions, a small number of technical changes have been made to some of the definitions as compared with the textbook version.  Most notably:
-- Sequences are indexed to start from zero rather than from one, as Mathlib has much more support for the 0-based natural numbers `ℕ` than the 1-based natural numbers.
-- Many operations that are left undefined in the text, such as division by zero, or taking the formal limit of a non-Cauchy sequence, are instead assigned a "junk" value (e.g., `0`) to make the operation totally defined.  This is because Lean has better support for total functions than partial functions (indiscriminate use of the latter can lead into "dependent type hell" in which even very basic manipulations require quite subtle and delicate proofs).  See for instance [this blog post](https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-theory-a-faq/) by Kevin Buzzard for more discussion.
-
-Currently formalized sections:
-
-- [Section 2.1: The Peano axioms](./sec21/)
-- [Section 2.2: Addition](./sec22/)
-- [Section 2.3: Multiplication](./sec23/)
-- [Chapter 2 epilogue: Isomorphism with the Mathlib natural numbers](./sec2e)
-- [Section 3.1: Set theory fundamentals](./sec31/)
-- [Section 3.2: Russel's paradox](./sec32/)
-- [Section 3.3: Functions](./sec33/)
-- [Section 3.4: Images and inverse images](./sec34/)
-- [Section 3.5: Cartesian products](./sec35/)
-- [Section 3.6: Cardinality of sets](./sec36/)
-- [Chapter 3 epilogue: Connections with ZFSet](./sec3e/)
-- [Section 4.1: The integers](./sec41/)
-- [Section 4.2: The rationals](./sec42/)
-- [Section 4.3: Absolute value and exponentiation](./sec43/)
-- [Section 4.4: Gaps in the rational numbers](./sec44/)
-- [Section 5.1: Cauchy sequences of rationals](./sec51)
-- [Section 5.2: Equivalent Cauchy sequences](./sec52/)
-- [Section 5.3: Construction of the real numbers](./sec53/)
-- [Section 5.4: Ordering the reals](./sec54/)
-- [Section 5.5: The least upper bound property](./sec55/)
-- [Section 5.6: Real exponentiation, part I](./sec56/)
-- [Chapter 5 epilogue: Isomorphism with the Mathlib reals](./sec5e/)
-- [Section 6.1: Convergence and limit laws](./sec61/)
-- [Section 6.2: The extended real number system](./sec62/)
-- [Section 6.3: Suprema and Infima of sequences](./sec63/)
-- [Section 6.4: Lim inf, lim sup, and limit points](./sec64/)
-- [Section 6.5: Some standard limits](./sec65/)
-- [Section 6.6: Subsequences](./sec66/)
-- [Section 6.7: Real exponentiation, part II](./sec67/)
-- [Section 6 epilogue: Connections with Mathlib limits](./sec6e/)
-- [Section 7.1: Finite series](./sec71/)
-- [Section 7.2: Infinite series](./sec72/)
-- [Section 7.3: Sums of non-negative numbers](./sec73/)
-- [Section 7.4: Rearrangement of series](./sec74/)
-- [Section 7.5: The root and ratio tests](./sec75/)
-- [Section 8.1: Countability](./sec81/)
-- [Section 8.2: Summation on infinite sets](./sec82/)
-- [Section 8.3: Uncountable sets](./sec83/)
-- [Section 8.4: The axiom of choice](./sec84/)
-- [Section 8.5: Ordered sets](./sec85/)
-- [Section 9.1: Subsets of the real line](./sec91/)
-- [Section 9.2: The algebra of real-valued functions](./sec92/)
-- [Section 9.3: Limiting values of functions](./sec93/)
-- [Section 9.4: Continuous functions](./sec94/)
-- [Section 9.5: Left and right limits](./sec95/)
-- [Section 9.6: The maximum principle](./sec96/)
-- [Section 9.7: The intermediate value theorem](./sec97/)
-- [Section 9.8: Monotone functions](./sec98/)
-- [Section 9.9: Uniform continuity](./sec99/)
-- [Section 9.10: Limits at infinity](./sec910/)
-- [Section 10.1: Basic definitions](./sec101/)
-- [Section 10.2: Local extrema and derivatives](./sec102/)
-- [Section 10.3: Monotone functions and derivatives](./sec103/)
-- [Section 10.4: The inverse function theorem](./sec104/)
-- [Section 10.5: L'Hôpital's rule](./sec105/)
-- [Section 11.1: Partitions](./sec111/)
-- [Section 11.2: Piecewise constant functions](./sec112/)
-- [Section 11.3: Upper and lower Riemann integrals](./sec113/)
-- [Section 11.4: Basic properties of the Riemann integral](./sec114/)
-- [Section 11.5: Riemann integrability of continuous functions](./sec115/)
-- [Section 11.6: Riemann integrability of monotone functions](./sec116/)
-- [Section 11.7: A non-Riemann integrable function](./sec117/)
-- [Section 11.8: The Riemann-Stieltjes integral](./sec118/)
-- [Section 11.9: The two fundamental theorems of calculus](./sec119/)
-- [Section 11.10: The fundamental theorem of calculus](./sec1110/)
-- [Appendix A.1: Mathematical statements](./appA1/)
-- [Appendix A.2: Implications](./appA2/)
-- [Appendix A.3: The structure of proofs](./appA3/)
-- [Appendix A.4: Variables and quantifiers](./appA4/)
-- [Appendix A.5: Nested quantifiers](./appA5/)
-- [Appendix A.6: Some examples of proofs and quantifiers](./appA6/)
-- [Appendix A.7: Equality](./appA7/)
-- [Appendix B.1: The decimal representation of natural numbers](./appB1/)
-- [Appendix B.2: The decimal representation of real numbers](./appB2/)
diff --git a/book/AnalysisBook/LiterateModule.lean b/book/AnalysisBook/LiterateModule.lean
deleted file mode 100644
index da91d888..00000000
--- a/book/AnalysisBook/LiterateModule.lean
+++ /dev/null
@@ -1,418 +0,0 @@
-import Lean.Data.Json
-import VersoBlog
-import SubVerso.Highlighting.Highlighted
-import SubVerso.Module
-import Std.Data.HashMap
-
-open Std
-open SubVerso.Module
-open SubVerso.Highlighting
-open Lean
-
-section
-variable [Monad m] [MonadError m] [MonadQuotation m]
-
-
-partial def getCommentString' (pref : String) (hl : Highlighted) : m String := do
-  let str := (← getString hl).trimAscii
-  let str := str.dropPrefix pref |>.dropSuffix "-/" |>.trimAscii
-  pure str.copy
-where getString : Highlighted → m String
-  | .text txt | .unparsed txt => pure txt
-  | .tactics .. => throwError "Tactics found in module docstring!"
-  | .point .. => pure ""
-  | .span _ hl => getCommentString' pref hl
-  | .seq hls => do return (← hls.mapM getString).foldl (init := "") (· ++ ·)
-  | .token ⟨_, txt⟩ => pure txt
-
-partial def getDocCommentString : Highlighted -> m String := getCommentString' "/--"
-end
-
-def loadModuleContent (mod : String) (leanProject : System.FilePath := "../analysis")
-    (overrideToolchain : Option String := none) : IO (Array (ModuleItem × Array (String × Highlighted))) := do
-
-  let projectDir := ((← IO.currentDir) / leanProject).normalize
-
-  -- Validate that the path is really a Lean project
-  let lakefile := projectDir / "lakefile.lean"
-  let lakefile' := projectDir / "lakefile.toml"
-  if !(← lakefile.pathExists <||> lakefile'.pathExists) then
-    throw <| .userError s!"Neither {lakefile} nor {lakefile'} exist, couldn't load project"
-  let lakeConfig := if (← lakefile.pathExists) then lakefile else lakefile'
-  let toolchain ← match overrideToolchain with
-    | none =>
-      let toolchainfile := projectDir / "lean-toolchain"
-      if !(← toolchainfile.pathExists) then
-        throw <| .userError s!"File {toolchainfile} doesn't exist, couldn't load project"
-      pure (← IO.FS.readFile toolchainfile).trimAscii.copy
-    | some override => pure override
-
-  -- Kludge: remove variables introduced by Lake. Clearing out DYLD_LIBRARY_PATH and
-  -- LD_LIBRARY_PATH is useful so the version selected by Elan doesn't get the wrong shared
-  -- libraries.
-  let lakeVars :=
-    #["LAKE", "LAKE_HOME", "LAKE_PKG_URL_MAP",
-      "LEAN_SYSROOT", "LEAN_AR", "LEAN_PATH", "LEAN_SRC_PATH",
-      "LEAN_GITHASH",
-      "ELAN_TOOLCHAIN", "DYLD_LIBRARY_PATH", "LD_LIBRARY_PATH"]
-
-  let f ← IO.FS.Handle.mk lakeConfig .read
-  f.lock (exclusive := true)
-  let jsonFile ←
-    try
-
-      let cmd := "elan"
-      let args := #["run", "--install", toolchain, "lake", "build", s!"+{mod}:literate"]
-
-      let res ← IO.Process.output {
-        cmd, args, cwd := projectDir
-        -- Unset Lake's environment variables
-        env := lakeVars.map (·, none)
-      }
-      if res.exitCode != 0 then
-        reportFail projectDir cmd args res
-
-      let args := #["run", "--install", toolchain, "lake", "query", s!"+{mod}:literate"]
-
-      let res ← IO.Process.output {
-        cmd, args, cwd := projectDir
-        -- Unset Lake's environment variables
-        env := lakeVars.map (·, none)
-      }
-      if res.exitCode != 0 then
-        reportFail projectDir cmd args res
-      IO.FS.readFile res.stdout.trimAscii.copy
-    finally f.unlock
-
-  let .ok (.arr json) := Json.parse jsonFile
-    | throw <| IO.userError s!"Expected JSON array"
-  match json.mapM deJson with
-  | .error err =>
-    throw <| IO.userError s!"Couldn't parse JSON from output file: {err}\nIn:\n{json}"
-  | .ok val => pure val
-
-where
-  deJson (v : Json) : Except String (ModuleItem × Array (String × Highlighted)) := do
-    let item ← FromJson.fromJson? (α := ModuleItem) v
-    let terms ← v.getObjVal? "terms"
-    let terms ← terms.getObj?
-    let terms ← terms.toArray.mapM fun ⟨k, v⟩ => (k, ·) <$> FromJson.fromJson? v
-    return (item, terms)
-  decorateOut (name : String) (out : String) : String :=
-    if out.isEmpty then "" else s!"\n{name}:\n{out}\n"
-  reportFail {α} (projectDir : System.FilePath) (cmd : String) (args : Array String) (res : IO.Process.Output) : IO α := do
-    IO.eprintln <|
-      "Build process failed." ++
-      "\nCWD: " ++ projectDir.toString ++
-      "\nCommand: " ++ cmd ++
-      "\nArgs: " ++ repr args ++
-      "\nExit code: " ++ toString res.exitCode ++
-      "\nstdout: " ++ res.stdout ++
-      "\nstderr: " ++ res.stderr
-
-    throw <| .userError <|
-      "Build process failed." ++
-      decorateOut "stdout" res.stdout ++
-      decorateOut "stderr" res.stderr
-
-open Verso.Genre.Blog Literate
-
-section
--- Some terms generated in the code, especially as part of proof goals, are very large, but also
--- repetitive. This causes a lot of overhead both for the Lean compiler and the C compiler. Instead
--- of compiling them to their representations as Lean code, they are saved in a de-duplicated JSON
--- serialization as a string literal. At run time, this is deserialized into the actual highlighted
--- term. This reduces the time spent compiling C from minutes to seconds and prevents the Lean compiler
--- from encountering resource limitations.
-
-open Meta
-open Elab Term
-
-variable [Monad m] [MonadLiftT CoreM m] [MonadLiftT MetaM m] [MonadLiftT TermElabM m] [MonadMCtx m] [MonadLiftT IO m]
-
-deriving instance ToExpr for Token.Kind
-deriving instance ToExpr for Token
-deriving instance ToExpr for Highlighted.Span.Kind
-
-initialize hlExportExt : EnvExtension Exporting ←
-  registerEnvExtension (pure {})
-
-
-def hlFromExport (exportLit : String) : Highlighted :=
-  match Json.parse exportLit with
-  | .error e => panic! s!"Failed to parse SubVerso export data as JSON: {e}"
-  | .ok v =>
-    match ExportCode.fromJson? v with
-    | .error e => panic! s!"Failed to deserialize SubVerso export data from parsed JSON: {e}"
-    | .ok v' =>
-      match v'.toHighlighted with
-      | .error e => panic! s!"Failed to deserialize highlighted code from export data: {e}"
-      | .ok hl => hl
-
-def hlViaExport (hl : Highlighted) : m Name := do
-  let exportedLit := hl.exportCode |>.toJson |>.compress
-  defineHl (← mkAppM ``hlFromExport #[toExpr exportedLit])
-where
-  hlType : Expr := .const ``Highlighted []
-  defineHl (hl : Expr) : TermElabM Name := withOptions (·.setBool `compiler.extract_closed false) do
-    let name ← Lean.mkFreshUserName `hlViaExport
-    addAndCompile <| .defnDecl {
-      name, type := hlType, value := hl,
-      levelParams := []
-      hints := .regular 0
-      safety := .safe
-    }
-    return name
-end
-
-def codeOpts : CodeOpts := { contextName := `name }
-
-open Verso Doc Elab PartElabM in
-open Verso.Genre Blog in
-open Lean.Parser.Command in
-partial def docFromModAndTerms
-    (config : LitPageConfig) (content : Array (ModuleItem × Array (String × Highlighted)))
-    (rewriter : Array (List Pat × List Literate.Template)) : PartElabM Unit := do
-  let mut mdHeaders : Array Nat := #[]
-  for cmd in content do
-    let ({kind, code, ..}, tms) := cmd
-    let tms := HashMap.emptyWithCapacity tms.size |>.insertMany tms
-    match kind with
-    | ``Lean.Parser.Module.header =>
-      if config.header then
-        addCodeBlock code
-      else pure ()
-    | ``moduleDoc =>
-      let str ← getModuleDocString code
-      let some ⟨mdBlocks⟩ := MD4Lean.parse str
-        | throwError m!"Failed to parse Markdown: {str}"
-      for b in mdBlocks do
-        match b with
-        | .header lvl txt =>
-          let inlines ← txt.mapM (ofInline tms)
-
-          if let some realLevel := mdHeaders.findRev? (· ≤ lvl) then
-            closePartsUntil realLevel ⟨0⟩ -- TODO endPos
-            mdHeaders := mdHeaders.take realLevel
-          else
-            mdHeaders := #[]
-
-          -- The new header could be a sibling or a child. If this is true, it's a child:
-          if !mdHeaders.back?.isEqSome lvl then
-            mdHeaders := mdHeaders.push lvl
-
-          push {
-            titleSyntax := (← arr inlines),
-            expandedTitle := some (txt.map inlineText |>.toList |> String.join, inlines),
-            metadata := none,
-            blocks := #[],
-            priorParts := #[]
-          }
-        | other =>
-          addBlock (← ofBlock tms other)
-          -- Only convert doccomments if the option is turned on
-    | ``declaration | `lemma =>
-      match code with
-      | .seq s =>
-        -- Find the index corresponding to the docComment
-        let docCommentIdx := s.findIdx? (fun
-          | (.token ⟨.docComment, _⟩) => true
-          | _ => false)
-        match docCommentIdx with
-        | some i =>
-          let codeBefore ← hlViaExport (Highlighted.seq s[:i])
-          let codeBefore ← ``(Verso.Doc.Block.other
-            (BlockExt.highlightedCode codeOpts $(mkIdent codeBefore)) Array.mkArray0)
-          let some ⟨mdBlocks⟩ := MD4Lean.parse (← getDocCommentString s[i]!)
-            | throwError m!"Failed to parse Markdown: {← getDocCommentString s[i]!}"
-          let docCommentBlocks ← mdBlocks.mapM (fun b => ofBlock tms b)
-          let codeAfter ← hlViaExport (Highlighted.seq s[i+1:])
-          let codeAfter ←``(Verso.Doc.Block.other (BlockExt.highlightedCode codeOpts $(mkIdent codeAfter)) Array.mkArray0)
-
-          let blocks : Array Term := #[codeBefore] ++ docCommentBlocks ++ #[codeAfter]
-          addBlock (← ``(Verso.Doc.Block.other (BlockExt.htmlDiv "declaration") #[$blocks,*]))
-        | none =>
-          -- No docComment attached to declaration, render definition as usual
-          addCodeBlock code
-          pure ()
-      | _ => addCodeBlock code
-        pure ()
-
-    | ``eval | ``evalBang | ``reduceCmd | ``print | ``printAxioms | ``printEqns | ``«where» | ``version | ``synth | ``check =>
-      -- addCodeBlock code
-      if let some msg := getFirstMessage code then
-        let msg : Highlighted.Message := ⟨msg.1, msg.2⟩
-        addBlock (← ``(Verso.Doc.Block.other (Blog.BlockExt.message false $(quote msg) []) #[]))
-    | _ =>
-      pure ()
-      addCodeBlock code
-  closePartsUntil 0 ⟨0⟩ -- TODO endPos?
-where
-  addCodeBlock (code : Highlighted) := do
-    let n ← hlViaExport code
-    addBlock (← ``(Verso.Doc.Block.other (BlockExt.highlightedCode codeOpts $(mkIdent n)) Array.mkArray0))
-
-  arr (xs : Array Term) : PartElabM Term := do
-    if xs.size ≤ 8 then
-      pure <| Syntax.mkCApp (`Array ++ s!"mkArray{xs.size}".toName) xs
-    else
-      `(#[$xs,*])
-
-  ofBlock (tms : HashMap String Highlighted) : MD4Lean.Block → PartElabM Term
-  | .header .. => throwError "Headers should be processed at the part level"
-  | .p txt => do
-    let inlines ← txt.mapM (ofInline tms)
-    ``(Verso.Doc.Block.para $(← arr inlines))
-  | .ul _ _ lis => do
-    ``(Verso.Doc.Block.ul $(← arr (← lis.mapM (ofLi tms))))
-  | .ol _ start _ lis => do
-    ``(Verso.Doc.Block.ol $(quote (start : Int)) $(← arr (← lis.mapM (ofLi tms))))
-  | .code info lang _ strs => do
-    let str := strs.toList |> String.join
-    if info.isEmpty && lang.isEmpty then
-      ``(Verso.Doc.Block.code $(quote str))
-    else
-      let msg : MessageData :=
-        "Info and language information in code blocks is not supported:" ++
-        indentD m!"info is {repr info} and language is {repr lang}"
-      throwError msg
-  | .blockquote bs => do
-    ``(Verso.Doc.Block.blockquote $(← arr (← bs.mapM (ofBlock tms))))
-  | b => throwError "Unsupported block {repr b}"
-
-  ofLi (tms : HashMap String Highlighted) : MD4Lean.Li MD4Lean.Block → PartElabM Term
-  | {isTask, taskChar:=_, taskMarkOffset:=_, contents} => do
-    if isTask then throwError "Tasks not supported"
-    ``(Verso.Doc.ListItem.mk $(← arr (← contents.mapM (ofBlock tms))))
-
-  ofInline (tms : HashMap String Highlighted) : MD4Lean.Text → PartElabM Term
-  | .normal str => ``(Verso.Doc.Inline.text $(quote str))
-  | .nullchar => throwError "Unsupported null character in Markdown"
-  | .softbr txt => ``(Verso.Doc.Inline.linebreak $(quote txt))
-  | .a href _title _isAuto contents => do
-    let href := (← href.mapM ofAttrText).toList |> String.join
-    let contents ← contents.mapM (ofInline tms)
-    ``(Verso.Doc.Inline.link $(← arr contents) $(quote href))
-  | .code str => do
-    let codeStr := String.join str.toList
-    if let some hl := tms[codeStr]? then
-      ``(Verso.Doc.Inline.other (InlineExt.highlightedCode codeOpts $(quote hl)) #[])
-    else
-      ``(Verso.Doc.Inline.code $(quote <| String.join str.toList))
-  | .em txt => do ``(Verso.Doc.Inline.emph $(← arr (← txt.mapM (ofInline tms))))
-  | .strong txt => do ``(Verso.Doc.Inline.bold $(← arr (← txt.mapM (ofInline tms))))
-  | .img src _title alt => do
-    let mut src := (← src.mapM ofAttrText).toList |> String.join
-    for (pat, template) in rewriter do
-      if let some ρ := Pat.match pat src then
-        src := ""
-        for t in template do
-          match t.subst ρ with
-          | .error e => throwError e
-          | .ok v => src := src ++ v
-        break
-    let alt := (alt.map inlineText).toList |> String.join
-    ``(Verso.Doc.Inline.image $(quote alt) $(quote src))
-  | .latexMath strs =>
-    let str := strs.toList |> String.join
-    ``(Verso.Doc.Inline.math MathMode.inline $(quote str))
-  | .latexMathDisplay strs =>
-    let str := strs.toList |> String.join
-    ``(Verso.Doc.Inline.math MathMode.display $(quote str))
-  | other => throwError "Unimplemented {repr other}"
-
-  inlineText : MD4Lean.Text → String
-  | .normal str
-  | .softbr str => str
-  | .em xs
-  | .strong xs
-  | .a _ _ _ xs => xs.map inlineText |>.toList |> String.join
-  | _ => ""
-
-  ofAttrText : MD4Lean.AttrText → PartElabM String
-  | .normal txt => pure txt
-  | other => throwError "Unimplemented {repr other}"
-
-
-
-open Verso Doc Concrete in
-open Lean Elab Command in
-open PartElabM in
-def elabAnalysisPage (x : Ident) (mod : Ident) (config : LitPageConfig) (title : StrLit) (genre : Term) (metadata? : Option Term) (rw : Option (TSyntax ``rewrites)) : CommandElabM Unit :=
-
-  withTraceNode `verso.blog.literate (fun _ => pure m!"Literate '{title.getString}'") do
-  let rewriter ← rw.mapM fun
-    | `(rewrites|rewriting $[| $cases]*) => cases.mapM Internal.getSubst
-    | rw => panic! s!"Unknown rewriter {rw}"
-
-  let rewriter := rewriter.getD #[]
-
-  let titleParts ← stringToInlines title
-  let titleString := inlinesToString (← getEnv) titleParts
-  let initState : PartElabM.State := .init (.node .none nullKind titleParts)
-
-  -- Each item pairs a top-level command with a mapping from terms found in docstrings to their
-  -- parsed, elaborated forms
-  let items ← withTraceNode `verso.blog.literate.loadMod (fun _ => pure m!"Loading '{mod}'") <|
-    loadModuleContent mod.getId.toString
-
-  let ctx ← runTermElabM fun _ => do
-    let g ← Term.elabTerm genre (some (.const ``Doc.Genre []))
-    pure { genreSyntax := genre
-           genre := g
-           refsAllowed := .onlyIfDefined
-           docReconstructionPlaceholder := some <| mkIdent (← mkFreshUserName `docReconst) : DocElabContext }
-  let ((), docState, partState) ← liftTermElabM <| PartElabM.run ctx {} initState <| do
-    setTitle titleString (← liftDocElabM <| titleParts.mapM (elabInline ⟨·⟩))
-    if let some metadata := metadata? then
-      modifyThe PartElabM.State fun st => {st with partContext.metadata := some metadata}
-
-    withTraceNode `verso.blog.literate.renderMod (fun _ => pure m!"Rendering '{mod}'") <|
-      docFromModAndTerms config items rewriter
-
-
-  let finished := partState.partContext.toPartFrame.close 0
-  let finished :=
-    -- Obey the Markdown convention of a single top-level header being the title of the document, if it's been followed
-    if let .mk _ _ _ metadata #[] #[p] _ := finished then
-      match p with
-      | .mk t1 t2 t3 _ bs ps pos =>
-        -- Propagate metadata fields
-        FinishedPart.mk t1 t2 t3 metadata bs ps pos
-      | _ => p
-    else finished
-
-  let ty ← ``(VersoDoc $genre)
-  let doc ← runTermElabM fun _ => finished.toVersoDoc genre ctx docState partState
-  elabCommand <| ← `(def $x : $ty := $doc)
-
-open Verso.Genre.Blog.Literate in
-open Lean.Parser.Tactic in
-/--
-Creates a page from a literate Lean module with Markdown module docstrings in it, performing a
-best-effort conversion from a large subset of Markdown to Verso documents. Inline code elements are
-elaborated as terms after the module itself; if they succeed, then they are highlighted as well. If
-not, they become ordinary Markdown code.
-
-Specifically, `def_literate_page PAGE from MOD in DIR as TITLE` defines a page `PAGE` by elaborating
-the module `MOD` in the project directory `DIR` with title `TITLE`.
-
-The literate Lean module does not need to use the same toolchain as Verso. `DIR` should be a project
-directory that contains a toolchain file and a Lake configuration (`lakefile.toml` or
-`lakefile.lean`), which should depend on the same version of SubVerso that Verso is using.
-
-Set the option `verso.literateMarkdown.logInlines` to `true` to see the error messages that
-prevented elaboration of inline elements.
--/
-syntax "analysis_page " ident optConfig " from " ident "  as " str (" with " term)? (rewrites)? : command
-
-open Verso Doc in
-open Lean Elab Command in
-open Verso.Genre.Blog Literate in
-elab_rules : command
-  | `(analysis_page $x $cfg:optConfig from $mod as $title $[with $metadata]? $[$rw:rewrites]?) => do
-    let (config, _) ← liftTermElabM <| do
-      litPageConfig cfg |>.run {elaborator := `x} |>.run {goals := []}
-    withScope (fun sc => {sc with opts := Elab.async.set sc.opts false}) do
-      let genre ← `(Page)
-      elabAnalysisPage x mod config title genre metadata rw
diff --git a/book/lake-manifest.json b/book/lake-manifest.json
deleted file mode 100644
index ac9dd0d7..00000000
--- a/book/lake-manifest.json
+++ /dev/null
@@ -1,45 +0,0 @@
-{"version": "1.1.0",
- "packagesDir": ".lake/packages",
- "packages":
- [{"url": "https://github.com/leanprover/verso.git",
-   "type": "git",
-   "subDir": null,
-   "scope": "",
-   "rev": "a6f65eae766f6ec01ab8e899efa261eb2ac34b68",
-   "name": "verso",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": false,
-   "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover-community/plausible",
-   "type": "git",
-   "subDir": null,
-   "scope": "",
-   "rev": "e84e3e16aea6b72cc5d311ca1bb25caad417e162",
-   "name": "plausible",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": true,
-   "configFile": "lakefile.toml"},
-  {"url": "https://github.com/acmepjz/md4lean",
-   "type": "git",
-   "subDir": null,
-   "scope": "",
-   "rev": "6a3fb240133bcb7e1a066fdc784b3fdc304e3fc5",
-   "name": "MD4Lean",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": true,
-   "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover/subverso",
-   "type": "git",
-   "subDir": null,
-   "scope": "",
-   "rev": "a86b5e65f79a705cf283fb1b05d547586e6d9c90",
-   "name": "subverso",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": true,
-   "configFile": "lakefile.lean"}],
- "name": "«analysis-book»",
- "lakeDir": ".lake"}
diff --git a/book/lakefile.lean b/book/lakefile.lean
deleted file mode 100644
index b1d7b811..00000000
--- a/book/lakefile.lean
+++ /dev/null
@@ -1,279 +0,0 @@
-import Lake
-open Lake DSL
-
--- This is set to `main` to get improvements made since the v4.23.0-rc2 tag. At the next Lean
--- version bump, switch this back to a versioned tag and delete this comment.
-require verso from git "https://github.com/leanprover/verso.git"@"main"
-
-package "analysis-book" where
-  version := v!"0.1.0"
-
-lean_lib «AnalysisBook» where
-  -- add library configuration options here
-
-@[default_target]
-lean_exe "analysis-book" where
-  root := `AnalysisBook
-
-/-- The root of the `analysis` project (used for HTML generation here) -/
-def analysisRoot : System.FilePath := "../analysis"
-
-/--
-A mapping from module names in the Lean code to the titles to be used for their sections.
-
-A module is generated for each, containing the literate page. Its name is the module name from
-`analysis` with `Book` prepended, so `Analysis.Section_2_1`'s literate page can be found by
-importing `Book.Analysis.Section_2_1`. The page itself is named identically to its module.
--/
-def sections := #[
-  (`Analysis.Section_2_1, "The Peano Axioms"),
-  (`Analysis.Section_2_2, "Addition"),
-  (`Analysis.Section_2_3, "Multiplication"),
-  (`Analysis.Section_2_epilogue, "Equivalence of naturals"),
-  (`Analysis.Section_3_1, "Fundamentals"),
-  (`Analysis.Section_3_2, "Russell's paradox"),
-  (`Analysis.Section_3_3, "Functions"),
-  (`Analysis.Section_3_4, "Images and inverse images"),
-  (`Analysis.Section_3_5, "Cartesian products"),
-  (`Analysis.Section_3_6, "Cardinality of sets"),
-  (`Analysis.Section_3_epilogue, "Connections with ZFSet"),
-  (`Analysis.Section_4_1, "The integers"),
-  (`Analysis.Section_4_2, "The rationals"),
-  (`Analysis.Section_4_3, "Absolute value and exponentiation"),
-  (`Analysis.Section_4_4, "Gaps in the rational numbers"),
-  (`Analysis.Section_5_1, "Cauchy sequences"),
-  (`Analysis.Section_5_2, "Equivalent Cauchy sequences"),
-  (`Analysis.Section_5_3, "The construction of the real numbers"),
-  (`Analysis.Section_5_4, "Ordering the reals"),
-  (`Analysis.Section_5_5, "The least upper bound property"),
-  (`Analysis.Section_5_6, "Real exponentiation, part I"),
-  (`Analysis.Section_5_epilogue, "Equivalence of reals"),
-  (`Analysis.Section_6_1, "Convergence and limit laws"),
-  (`Analysis.Section_6_2, "The extended real number system"),
-  (`Analysis.Section_6_3, "Suprema and Infima of sequences"),
-  (`Analysis.Section_6_4, "Limsup, Liminf, and limit points"),
-  (`Analysis.Section_6_5, "Some standard limits"),
-  (`Analysis.Section_6_6, "Subsequences"),
-  (`Analysis.Section_6_7, "Real exponentiation, part II"),
-  (`Analysis.Section_6_epilogue, "Connections with Mathlib limits"),
-  (`Analysis.Section_7_1, "Finite series"),
-  (`Analysis.Section_7_2, "Infinite series"),
-  (`Analysis.Section_7_3, "Sums of non-negative numbers"),
-  (`Analysis.Section_7_4, "Rearrangement of series"),
-  (`Analysis.Section_7_5, "The root and ratio tests"),
-  (`Analysis.Section_8_1, "Countability"),
-  (`Analysis.Section_8_2, "Summation on infinite sets"),
-  (`Analysis.Section_8_3, "Uncountable sets"),
-  (`Analysis.Section_8_4, "The axiom of choice"),
-  (`Analysis.Section_8_5, "Ordered sets"),
-  (`Analysis.Section_9_1, "Subsets of the real line"),
-  (`Analysis.Section_9_2, "The algebra of real-valued functions"),
-  (`Analysis.Section_9_3, "Limiting values of functions"),
-  (`Analysis.Section_9_4, "Continuous functions"),
-  (`Analysis.Section_9_5, "Limits from the left and right"),
-  (`Analysis.Section_9_6, "The maximum principle"),
-  (`Analysis.Section_9_7, "The intermediate value theorem"),
-  (`Analysis.Section_9_8, "Monotone functions"),
-  (`Analysis.Section_9_9, "Uniform continuity"),
-  (`Analysis.Section_9_10, "Limits at infinity"),
-  (`Analysis.Section_10_1, "Basic definitions"),
-  (`Analysis.Section_10_2, "Local maxima, local minima, and derivatives"),
-  (`Analysis.Section_10_3, "Monotone functions and derivatives"),
-  (`Analysis.Section_10_4, "The inverse function theorem"),
-  (`Analysis.Section_10_5, "L'Hôpital's rule"),
-  (`Analysis.Section_11_1, "Partitions"),
-  (`Analysis.Section_11_2, "Piecewise constant functions"),
-  (`Analysis.Section_11_3, "Upper and lower Riemann integrals"),
-  (`Analysis.Section_11_4, "Basic properties of the Riemann integral"),
-  (`Analysis.Section_11_5, "Riemann integrability of continuous functions"),
-  (`Analysis.Section_11_6, "Riemann integrability of monotone functions"),
-  (`Analysis.Section_11_7, "A non-Riemann integrable function"),
-  (`Analysis.Section_11_8, "The Riemann-Stieltjes integral"),
-  (`Analysis.Section_11_9, "The two fundamental theorems of calculus"),
-  (`Analysis.Section_11_10, "Consequences of the fundamental theorem of calculus"),
-  (`Analysis.Section_9_1, "Subsets of the real line"),
-  (`Analysis.Section_9_2, "The algebra of real-valued functions"),
-  (`Analysis.Section_9_3, "Limiting values of functions"),
-  (`Analysis.Section_9_4, "Continuous functions"),
-  (`Analysis.Section_9_5, "Limits from the left and right"),
-  (`Analysis.Section_9_6, "The maximum principle"),
-  (`Analysis.Section_9_7, "The intermediate value theorem"),
-  (`Analysis.Section_9_8, "Monotone functions"),
-  (`Analysis.Section_9_9, "Uniform continuity"),
-  (`Analysis.Section_9_10, "Limits at infinity"),
-  (`Analysis.Section_10_1, "Basic definitions"),
-  (`Analysis.Section_10_2, "Local maxima, local minima, and derivatives"),
-  (`Analysis.Section_10_3, "Monotone functions and derivatives"),
-  (`Analysis.Section_10_4, "The inverse function theorem"),
-  (`Analysis.Section_10_5, "L'Hôpital's rule"),
-  (`Analysis.Section_11_1, "Partitions"),
-  (`Analysis.Section_11_2, "Piecewise constant functions"),
-  (`Analysis.Section_11_3, "Upper and lower Riemann integrals"),
-  (`Analysis.Section_11_4, "Basic properties of the Riemann integral"),
-  (`Analysis.Section_11_5, "Riemann integrability of continuous functions"),
-  (`Analysis.Section_11_6, "Riemann integrability of monotone functions"),
-  (`Analysis.Section_11_7, "A non-Riemann integrable function"),
-  (`Analysis.Section_11_8, "The Riemann-Stieltjes integral"),
-  (`Analysis.Section_11_9, "The two fundamental theorems of calculus"),
-  (`Analysis.Section_11_10, "Consequences of the fundamental theorem of calculus"),
-  (`Analysis.Section_9_1, "Subsets of the real line"),
-  (`Analysis.Section_9_2, "The algebra of real-valued functions"),
-  (`Analysis.Section_9_3, "Limiting values of functions"),
-  (`Analysis.Section_9_4, "Continuous functions"),
-  (`Analysis.Section_9_5, "Limits from the left and right"),
-  (`Analysis.Section_9_6, "The maximum principle"),
-  (`Analysis.Section_9_7, "The intermediate value theorem"),
-  (`Analysis.Section_9_8, "Monotone functions"),
-  (`Analysis.Section_9_9, "Uniform continuity"),
-  (`Analysis.Section_9_10, "Limits at infinity"),
-  (`Analysis.Section_10_1, "Basic definitions"),
-  (`Analysis.Section_10_2, "Local maxima, local minima, and derivatives"),
-  (`Analysis.Section_10_3, "Monotone functions and derivatives"),
-  (`Analysis.Section_10_4, "The inverse function theorem"),
-  (`Analysis.Section_10_5, "L'Hôpital's rule"),
-  (`Analysis.Section_11_1, "Partitions"),
-  (`Analysis.Section_11_2, "Piecewise constant functions"),
-  (`Analysis.Section_11_3, "Upper and lower Riemann integrals"),
-  (`Analysis.Section_11_4, "Basic properties of the Riemann integral"),
-  (`Analysis.Section_11_5, "Riemann integrability of continuous functions"),
-  (`Analysis.Section_11_6, "Riemann integrability of monotone functions"),
-  (`Analysis.Section_11_7, "A non-Riemann integrable function"),
-  (`Analysis.Section_11_8, "The Riemann-Stieltjes integral"),
-  (`Analysis.Section_11_9, "The two fundamental theorems of calculus"),
-  (`Analysis.Section_11_10, "Consequences of the fundamental theorem of calculus"),
-  (`Analysis.Appendix_A_1, "Mathematical statements"),
-  (`Analysis.Appendix_A_2, "Implication"),
-  (`Analysis.Appendix_A_3, "The structure of proofs"),
-  (`Analysis.Appendix_A_4, "Variables and quantifiers"),
-  (`Analysis.Appendix_A_5, "Nested quantifiers"),
-  (`Analysis.Appendix_A_6, "Some examples of proofs and quantifiers"),
-  (`Analysis.Appendix_A_7, "Equality"),
-  (`Analysis.Appendix_B_1, "The decimal representation of natural numbers"),
-  (`Analysis.Appendix_B_2, "The decimal representation of real numbers")
-]
-
-/--
-Generates the JSON representation of the data needed for the literate page for the given module.
-
-This is called as needed if the module has changed.
--/
-def buildLiterateJson (pkg : NPackage n) (mod : String) : LogIO Unit := do
-  let lakeVars :=
-    #["LAKE", "LAKE_HOME", "LAKE_PKG_URL_MAP",
-      "LEAN_SYSROOT", "LEAN_AR", "LEAN_PATH", "LEAN_SRC_PATH",
-      "LEAN_GITHASH",
-      "ELAN_TOOLCHAIN", "DYLD_LIBRARY_PATH", "LD_LIBRARY_PATH"]
-
-  let lakefile := pkg.dir / analysisRoot / "lakefile.lean"
-  let lakefile' := pkg.dir / analysisRoot / "lakefile.toml"
-  let lakeConfig := if (← lakefile.pathExists) then lakefile else lakefile'
-
-
-  let toolchainFile := pkg.dir / analysisRoot / "lean-toolchain"
-  let toolchain := (← IO.FS.readFile toolchainFile).trim
-
-  let f ← IO.FS.Handle.mk lakeConfig .read
-  -- The locking here and in the generator prevent concurrent builds from interfering
-  f.lock (exclusive := true)
-  try
-    let cmd := "elan"
-
-    let args := #["run", "--install", toolchain, "lake", "build", s!"+{mod}:literate"]
-
-    proc (quiet := true) {
-      cmd, args, cwd := pkg.dir / analysisRoot,
-      -- Unset Lake's environment variables
-      env := lakeVars.map (·, none)
-    }
-
-  finally
-    f.unlock
-
-
-/-
-**NOTE:** `genLib` needs to be built separately if an old version of
-any of the generated modules with the correct imports does not yet exist.
-
-This is because Lake currently traverses module imports before waiting on the
-library's extra dependencies (i.e., the `genLib` job when part of `needs`).
-This should fixed in a future Lake.
--/
-target genLib (pkg) : Unit := do
-  let j1 ← Job.mixArray <$> sections.mapM fun (module, title) => Job.async do
-    let leanModName := `Book ++ module
-    let declName := `Book ++ module
-    -- This will fail if the `Book` library (below) is not defined
-    let some mod ← findModule? leanModName
-      | error s!"Failed to generate {leanModName}:\
-          It has not been defined in the workspace."
-
-    -- Get the name of the original Lean file that gives the chapter its content
-    let origName := "/".intercalate (module.components.map (·.toString)) ++ ".lean"
-    let origLeanFile : System.FilePath := pkg.dir / analysisRoot / origName
-    -- Changes to the original Lean file should invalidate the generated code
-    addTrace (← computeTrace <| TextFilePath.mk origLeanFile)
-
-    -- We need to generate a file to represent the fact that the JSON was updated in the main
-    -- project. This serves as a kind of proxy for Lake.
-    let jsonSentinel := defaultBuildDir / "originals" / module.toString
-
-    let jsonName := "/".intercalate (module.components.map (·.toString)) ++ ".json"
-    let jsonFile : System.FilePath := pkg.dir / analysisRoot / ".lake" / "build" / "literate" / jsonName
-    -- If the build directory in ../analysis is deleted, we need to regenerate these files. This
-    -- trace ensures that the files' absence is noticed.
-    addPureTrace (caption := "{jsonFile} exists") (← jsonFile.pathExists)
-
-    buildFileUnlessUpToDate' jsonSentinel do
-      logVerbose s!"Generating highlighting info for {module}"
-      buildLiterateJson pkg module.toString
-      logVerbose s!"Built module's JSON"
-      -- Now that the JSON file definitely exists, add its dependencies to the sentinel's
-      let trace ← computeTrace (TextFilePath.mk jsonFile)
-      addTrace trace
-      createParentDirs jsonSentinel
-      -- This content doesn't really matter, but it makes debugging simpler
-      IO.FS.writeFile jsonSentinel (toString (repr trace))
-
-
-
-    -- The module itself contains the literate page
-    let contents := s!"import AnalysisBook.LiterateModule\n\nset_option maxHeartbeats 100000000\n\nset_option maxRecDepth 20000\n\nanalysis_page {declName} from {module} as {repr title}\n"
-    addPureTrace contents "contents"
-
-    buildFileUnlessUpToDate' mod.leanFile do
-      logVerbose s!"Generating {mod.leanFile}"
-      createParentDirs mod.leanFile
-      IO.FS.writeFile mod.leanFile contents
-      -- invalidate the module's build
-      liftM (m := IO) <| try IO.FS.removeFile mod.oleanFile catch
-        | .noFileOrDirectory .. => pure ()
-        | e => throw e
-
-  -- Also build a root module that imports all the modules, to avoid having to do it by hand in the
-  -- main module
-  let j2 ← Job.async do
-    let rootName := `Book
-    let some mod ← findModule? rootName
-      | error s!"Failed to generate {rootName}:\
-          It has not been defined in the workspace."
-    let mut contents := ""
-    for (module, title) in sections do
-      contents := contents ++ s!"import {`Book ++ module} -- {title}\n"
-    addPureTrace contents "contents"
-    buildFileUnlessUpToDate' mod.leanFile do
-      logVerbose s!"Generating {mod.leanFile}"
-      createParentDirs mod.leanFile
-      IO.FS.writeFile mod.leanFile contents
-      -- invalidate the module's build
-      liftM (m := IO) <| try IO.FS.removeFile mod.oleanFile catch
-        | .noFileOrDirectory .. => pure ()
-        | e => throw e
-  pure <| Job.mix j1 j2
-
-/-- Blocking until the job completes avoids the above caveat. -/
-target genLibSync : Unit := do
-  .pure <$> (← genLib.fetch).await
-
-lean_lib Book where
-  needs := #[genLibSync]
-  srcDir := defaultBuildDir / "src"
diff --git a/book/lean-toolchain b/book/lean-toolchain
deleted file mode 100644
index bf718850..00000000
--- a/book/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:v4.29.0-rc6
\ No newline at end of file
diff --git a/book/static_files/style.css b/book/static_files/style.css
deleted file mode 100644
index 6c09f6d8..00000000
--- a/book/static_files/style.css
+++ /dev/null
@@ -1,66 +0,0 @@
-nav {
-    position: fixed;
-    top: 0;
-    left: 0;
-    width: 14em;
-    height: 100vh;
-    background: #f7f7fa;
-    border-right: 1px solid #ddd;
-    padding: 2em 1em 1em 1em;
-    box-sizing: border-box;
-    overflow-y: auto;
-    z-index: 100;
-}
-
-nav ol {
-    list-style: none;
-    padding: 0;
-    margin: 0;
-}
-
-nav ol li {
-    margin-bottom: 1em;
-}
-
-nav ol li a {
-    display: block;
-    color: #222;
-    text-decoration: none;
-    padding: 0.5em 0.75em;
-    border-radius: 4px;
-    transition: background 0.2s;
-}
-
-nav ol li a:hover,
-nav ol li a:focus {
-    background: #e0e0f0;
-    color: #000;
-}
-
-/* Add left margin to main content to avoid overlap */
-header,
-div.main {
-    margin-left: 16em;
-}
-
-code span {
-    font-family: "Source Code Pro" "Noto sans mono", monospace;
-    font-size: 15px;
-}
-
-body {
-    font-family: "Source Sans 3","Helvetica Neue","Segoe UI","Roboto",Arial,sans-serif;
-}
-
-div.declaration {
-    border-top: 1px solid #c0c0d0;
-    padding-top: 1em;
-    padding-bottom: 1em;
-    margin-top: 1em;
-    margin-bottom: 1em;
-}
-
-/* HACK: disable wavy red underline for errors, because they are quite common in docstrings */
-.hl.lean .has-info.error :not(.tactic-state):not(.tactic-state *) {
-    text-decoration: none !important;
-}
diff --git a/build-web.sh b/build-web.sh
index 6eb3d490..b0e038e3 100755
--- a/build-web.sh
+++ b/build-web.sh
@@ -4,10 +4,7 @@
 
 set -o pipefail # stop if any command fails
 
-cd analysis/
 lake exe cache get
 lake -R -Kenv=dev build Analysis:docs
 lake build
-cd ../book/
-lake exe analysis-book
-cd ../
+lake build :literateHtml
diff --git a/build.sh b/build.sh
index 43ea3be8..d7b90272 100755
--- a/build.sh
+++ b/build.sh
@@ -4,6 +4,5 @@
 
 set -o pipefail # stop if any command fails
 
-cd analysis/
 lake exe cache get
 lake build
\ No newline at end of file
diff --git a/analysis/lake-manifest.json b/lake-manifest.json
similarity index 81%
rename from analysis/lake-manifest.json
rename to lake-manifest.json
index c771d459..b0c25c6c 100644
--- a/analysis/lake-manifest.json
+++ b/lake-manifest.json
@@ -5,38 +5,28 @@
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "5c8398df528176d9c87ccd9226ba8f7c8852d59c",
+   "rev": "698d2b68b870f1712040ab0c233d34372d4b56df",
    "name": "mathlib",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v4.29.0-rc6",
+   "inputRev": "v4.29.0-rc8",
    "inherited": false,
    "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover/doc-gen4",
-   "type": "git",
-   "subDir": null,
-   "scope": "",
-   "rev": "f5f957cf052287676783478feec60f7ddf757c0a",
-   "name": "«doc-gen4»",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": false,
-   "configFile": "lakefile.lean"},
-  {"url": "https://github.com/acmepjz/md4lean",
+  {"url": "https://github.com/leanprover/verso",
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "6a3fb240133bcb7e1a066fdc784b3fdc304e3fc5",
-   "name": "MD4Lean",
+   "rev": "b6a5bacc221b260a67d474a2436b89d067ae5f7d",
+   "name": "verso",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
    "inherited": false,
    "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover/subverso",
+  {"url": "https://github.com/leanprover/doc-gen4",
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "a86b5e65f79a705cf283fb1b05d547586e6d9c90",
-   "name": "subverso",
+   "rev": "fbfa185b60c17f8efb9c78863ccf3cf873b6721b",
+   "name": "«doc-gen4»",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
    "inherited": false,
@@ -45,7 +35,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "e84e3e16aea6b72cc5d311ca1bb25caad417e162",
+   "rev": "22a0afa903bcf65285152eea298a3d319badc78d",
    "name": "plausible",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -65,7 +55,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "f207d9fcf0cef00ba79962a33ef156061914d9c7",
+   "rev": "db22912cdd820b2a2bd84bd25273cb322ff09ead",
    "name": "importGraph",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -75,17 +65,17 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "2e58165a9dcdca9837b666528f974299ee1a51cc",
+   "rev": "136730b5a40dc633967f5433cb7668df5c3bf9a3",
    "name": "proofwidgets",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v0.0.92",
+   "inputRev": "v0.0.94",
    "inherited": true,
    "configFile": "lakefile.lean"},
   {"url": "https://github.com/leanprover-community/aesop",
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "c3361708f266893de5d1769192b60d4b1831f2bb",
+   "rev": "3426969888a264d3f69b6f30ab50aa11f28eb38d",
    "name": "aesop",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -95,7 +85,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "221e8088e3a066b8676dc471ff10638cf1c10835",
+   "rev": "3a9fde028258300f1cbb003d457d47c8d8e16b1c",
    "name": "Qq",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -105,7 +95,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "bd58e3506632241b59e406902d5e42b73cdeccce",
+   "rev": "bce25af79ec73f5e63240d4399a4cd8a6a227fcb",
    "name": "batteries",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -115,12 +105,32 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover",
-   "rev": "3de531c1135f5e3a01f3ac04830996fda476b28e",
+   "rev": "61cd682f2a25175996bc1b9e8d8231e76cded866",
    "name": "Cli",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v4.29.0-rc6",
+   "inputRev": "v4.29.0-rc8",
    "inherited": true,
    "configFile": "lakefile.toml"},
+  {"url": "https://github.com/acmepjz/md4lean",
+   "type": "git",
+   "subDir": null,
+   "scope": "",
+   "rev": "6a3fb240133bcb7e1a066fdc784b3fdc304e3fc5",
+   "name": "MD4Lean",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "main",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover/subverso",
+   "type": "git",
+   "subDir": null,
+   "scope": "",
+   "rev": "52b9dfbd2658408e37ae6e8b72601ddeaaa25a0c",
+   "name": "subverso",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "main",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
   {"url": "https://github.com/kim-em/leansqlite",
    "type": "git",
    "subDir": null,
@@ -135,7 +145,7 @@
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "d7f24379ba37ec711f3f96b7187ca8dcc98b20e3",
+   "rev": "629254926fb54ef83d582bd41a0b9eb72b934015",
    "name": "UnicodeBasic",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
diff --git a/lakefile.lean b/lakefile.lean
new file mode 100644
index 00000000..ffb44c15
--- /dev/null
+++ b/lakefile.lean
@@ -0,0 +1,29 @@
+import Lake
+open Lake DSL
+
+package «Analysis» where
+  -- Settings applied to both builds and interactive editing
+  leanOptions := #[
+    ⟨`pp.unicode.fun, true⟩, -- pretty-prints `fun a ↦ b`
+    ⟨`doc.verso, true⟩ -- use Verso-format docstrings
+  ]
+  -- Settings applied only to command line builds
+  moreLeanArgs := #[
+    "-Dwarn.sorry=false" -- suppress warnings about `sorry` on the command line; remove when project is complete
+  ]
+  -- add any additional package configuration options here
+
+meta if get_config? env = some "dev" then
+require «doc-gen4» from git "https://github.com/leanprover/doc-gen4" @ "main"
+
+require verso from git
+  "https://github.com/leanprover/verso" @ "main"
+
+-- Require Mathlib (the comprehensive library of mathematics in Lean)
+require mathlib from git
+  "https://github.com/leanprover-community/mathlib4.git" @ "v4.29.0-rc8"
+
+
+@[default_target]
+lean_lib «Analysis» where
+  -- add any library configuration options here
diff --git a/lean-toolchain b/lean-toolchain
new file mode 100644
index 00000000..b58ff4f0
--- /dev/null
+++ b/lean-toolchain
@@ -0,0 +1 @@
+leanprover/lean4:v4.29.0-rc8
\ No newline at end of file
diff --git a/literate.toml b/literate.toml
new file mode 100644
index 00000000..697f1ead
--- /dev/null
+++ b/literate.toml
@@ -0,0 +1,303 @@
+exclude = ["Analysis.Misc", "Analysis.MeasureTheory"]
+docstrings_as_text = true
+landing_page = "Analysis"
+
+[order_children]
+"Analysis" = [
+  "Analysis.Section_2_1",
+  "Analysis.Section_2_2",
+  "Analysis.Section_2_3",
+  "Analysis.Section_2_epilogue",
+  "Analysis.Section_3_1",
+  "Analysis.Section_3_2",
+  "Analysis.Section_3_3",
+  "Analysis.Section_3_4",
+  "Analysis.Section_3_5",
+  "Analysis.Section_3_6",
+  "Analysis.Section_3_epilogue",
+  "Analysis.Section_4_1",
+  "Analysis.Section_4_2",
+  "Analysis.Section_4_3",
+  "Analysis.Section_4_4",
+  "Analysis.Section_5_1",
+  "Analysis.Section_5_2",
+  "Analysis.Section_5_3",
+  "Analysis.Section_5_4",
+  "Analysis.Section_5_5",
+  "Analysis.Section_5_6",
+  "Analysis.Section_5_epilogue",
+  "Analysis.Section_6_1",
+  "Analysis.Section_6_2",
+  "Analysis.Section_6_3",
+  "Analysis.Section_6_4",
+  "Analysis.Section_6_5",
+  "Analysis.Section_6_6",
+  "Analysis.Section_6_7",
+  "Analysis.Section_6_epilogue",
+  "Analysis.Section_7_1",
+  "Analysis.Section_7_2",
+  "Analysis.Section_7_3",
+  "Analysis.Section_7_4",
+  "Analysis.Section_7_5",
+  "Analysis.Section_8_1",
+  "Analysis.Section_8_2",
+  "Analysis.Section_8_3",
+  "Analysis.Section_8_4",
+  "Analysis.Section_8_5",
+  "Analysis.Section_9_1",
+  "Analysis.Section_9_2",
+  "Analysis.Section_9_3",
+  "Analysis.Section_9_4",
+  "Analysis.Section_9_5",
+  "Analysis.Section_9_6",
+  "Analysis.Section_9_7",
+  "Analysis.Section_9_8",
+  "Analysis.Section_9_9",
+  "Analysis.Section_9_10",
+  "Analysis.Section_10_1",
+  "Analysis.Section_10_2",
+  "Analysis.Section_10_3",
+  "Analysis.Section_10_4",
+  "Analysis.Section_10_5",
+  "Analysis.Section_11_1",
+  "Analysis.Section_11_2",
+  "Analysis.Section_11_3",
+  "Analysis.Section_11_4",
+  "Analysis.Section_11_5",
+  "Analysis.Section_11_6",
+  "Analysis.Section_11_7",
+  "Analysis.Section_11_8",
+  "Analysis.Section_11_9",
+  "Analysis.Section_11_10",
+  "Analysis.Appendix_A_1",
+  "Analysis.Appendix_A_2",
+  "Analysis.Appendix_A_3",
+  "Analysis.Appendix_A_4",
+  "Analysis.Appendix_A_5",
+  "Analysis.Appendix_A_6",
+  "Analysis.Appendix_A_7",
+  "Analysis.Appendix_B_1",
+  "Analysis.Appendix_B_2",
+]
+
+[modules."Analysis.Section_2_1"]
+title = "2.1. The Peano Axioms"
+
+[modules."Analysis.Section_2_2"]
+title = "2.2. Addition"
+
+[modules."Analysis.Section_2_3"]
+title = "2.3. Multiplication"
+
+[modules."Analysis.Section_2_epilogue"]
+title = "2. (epilogue) Equivalence of naturals"
+
+[modules."Analysis.Section_3_1"]
+title = "3.1. Fundamentals"
+
+[modules."Analysis.Section_3_2"]
+title = "3.2. Russell's paradox"
+
+[modules."Analysis.Section_3_3"]
+title = "3.3. Functions"
+
+[modules."Analysis.Section_3_4"]
+title = "3.4. Images and inverse images"
+
+[modules."Analysis.Section_3_5"]
+title = "3.5. Cartesian products"
+
+[modules."Analysis.Section_3_6"]
+title = "3.6. Cardinality of sets"
+
+[modules."Analysis.Section_3_epilogue"]
+title = "3. (epilogue) Connections with ZFSet"
+
+[modules."Analysis.Section_4_1"]
+title = "4.1. The integers"
+
+[modules."Analysis.Section_4_2"]
+title = "4.2. The rationals"
+
+[modules."Analysis.Section_4_3"]
+title = "4.3. Absolute value and exponentiation"
+
+[modules."Analysis.Section_4_4"]
+title = "4.4. Gaps in the rational numbers"
+
+[modules."Analysis.Section_5_1"]
+title = "5.1. Cauchy sequences"
+
+[modules."Analysis.Section_5_2"]
+title = "5.2. Equivalent Cauchy sequences"
+
+[modules."Analysis.Section_5_3"]
+title = "5.3. The construction of the real numbers"
+
+[modules."Analysis.Section_5_4"]
+title = "5.4. Ordering the reals"
+
+[modules."Analysis.Section_5_5"]
+title = "5.5. The least upper bound property"
+
+[modules."Analysis.Section_5_6"]
+title = "5.6. Real exponentiation, part I"
+
+[modules."Analysis.Section_5_epilogue"]
+title = "5. (epilogue) Equivalence of reals"
+
+[modules."Analysis.Section_6_1"]
+title = "6.1. Convergence and limit laws"
+
+[modules."Analysis.Section_6_2"]
+title = "6.2. The extended real number system"
+
+[modules."Analysis.Section_6_3"]
+title = "6.3. Suprema and Infima of sequences"
+
+[modules."Analysis.Section_6_4"]
+title = "6.4. Limsup, Liminf, and limit points"
+
+[modules."Analysis.Section_6_5"]
+title = "6.5. Some standard limits"
+
+[modules."Analysis.Section_6_6"]
+title = "6.6. Subsequences"
+
+[modules."Analysis.Section_6_7"]
+title = "6.7. Real exponentiation, part II"
+
+[modules."Analysis.Section_6_epilogue"]
+title = "6. (epilogue) Connections with Mathlib limits"
+
+[modules."Analysis.Section_7_1"]
+title = "7.1. Finite series"
+
+[modules."Analysis.Section_7_2"]
+title = "7.2. Infinite series"
+
+[modules."Analysis.Section_7_3"]
+title = "7.3. Sums of non-negative numbers"
+
+[modules."Analysis.Section_7_4"]
+title = "7.4. Rearrangement of series"
+
+[modules."Analysis.Section_7_5"]
+title = "7.5. The root and ratio tests"
+
+[modules."Analysis.Section_8_1"]
+title = "8.1. Countability"
+
+[modules."Analysis.Section_8_2"]
+title = "8.2. Summation on infinite sets"
+
+[modules."Analysis.Section_8_3"]
+title = "8.3. Uncountable sets"
+
+[modules."Analysis.Section_8_4"]
+title = "8.4. The axiom of choice"
+
+[modules."Analysis.Section_8_5"]
+title = "8.5. Ordered sets"
+
+[modules."Analysis.Section_9_1"]
+title = "9.1. Subsets of the real line"
+
+[modules."Analysis.Section_9_2"]
+title = "9.2. The algebra of real-valued functions"
+
+[modules."Analysis.Section_9_3"]
+title = "9.3. Limiting values of functions"
+
+[modules."Analysis.Section_9_4"]
+title = "9.4. Continuous functions"
+
+[modules."Analysis.Section_9_5"]
+title = "9.5. Limits from the left and right"
+
+[modules."Analysis.Section_9_6"]
+title = "9.6. The maximum principle"
+
+[modules."Analysis.Section_9_7"]
+title = "9.7. The intermediate value theorem"
+
+[modules."Analysis.Section_9_8"]
+title = "9.8. Monotone functions"
+
+[modules."Analysis.Section_9_9"]
+title = "9.9. Uniform continuity"
+
+[modules."Analysis.Section_9_10"]
+title = "9.10. Limits at infinity"
+
+[modules."Analysis.Section_10_1"]
+title = "10.1. Basic definitions"
+
+[modules."Analysis.Section_10_2"]
+title = "10.2. Local maxima, local minima, and derivatives"
+
+[modules."Analysis.Section_10_3"]
+title = "10.3. Monotone functions and derivatives"
+
+[modules."Analysis.Section_10_4"]
+title = "10.4. The inverse function theorem"
+
+[modules."Analysis.Section_10_5"]
+title = "10.5. L'Hôpital's rule"
+
+[modules."Analysis.Section_11_1"]
+title = "11.1. Partitions"
+
+[modules."Analysis.Section_11_2"]
+title = "11.2. Piecewise constant functions"
+
+[modules."Analysis.Section_11_3"]
+title = "11.3. Upper and lower Riemann integrals"
+
+[modules."Analysis.Section_11_4"]
+title = "11.4. Basic properties of the Riemann integral"
+
+[modules."Analysis.Section_11_5"]
+title = "11.5. Riemann integrability of continuous functions"
+
+[modules."Analysis.Section_11_6"]
+title = "11.6. Riemann integrability of monotone functions"
+
+[modules."Analysis.Section_11_7"]
+title = "11.7. A non-Riemann integrable function"
+
+[modules."Analysis.Section_11_8"]
+title = "11.8. The Riemann-Stieltjes integral"
+
+[modules."Analysis.Section_11_9"]
+title = "11.9. The two fundamental theorems of calculus"
+
+[modules."Analysis.Section_11_10"]
+title = "11.10. Consequences of the fundamental theorem of calculus"
+
+[modules."Analysis.Appendix_A_1"]
+title = "A.1. Mathematical statements"
+
+[modules."Analysis.Appendix_A_2"]
+title = "A.2. Implication"
+
+[modules."Analysis.Appendix_A_3"]
+title = "A.3. The structure of proofs"
+
+[modules."Analysis.Appendix_A_4"]
+title = "A.4. Variables and quantifiers"
+
+[modules."Analysis.Appendix_A_5"]
+title = "A.5. Nested quantifiers"
+
+[modules."Analysis.Appendix_A_6"]
+title = "A.6. Some examples of proofs and quantifiers"
+
+[modules."Analysis.Appendix_A_7"]
+title = "A.7. Equality"
+
+[modules."Analysis.Appendix_B_1"]
+title = "B.1. The decimal representation of natural numbers"
+
+[modules."Analysis.Appendix_B_2"]
+title = "B.2. The decimal representation of real numbers"
diff --git a/serve.py b/serve.py
index 3da5f536..e45c56c1 100644
--- a/serve.py
+++ b/serve.py
@@ -4,8 +4,8 @@
 import urllib
 from http import HTTPStatus
 
-BOOK_SITE = os.path.abspath('./book/_site')
-DOCS_SITE = os.path.abspath('./analysis/.lake/build/doc')
+BOOK_SITE = os.path.abspath('./.lake/build/literate-html')
+DOCS_SITE = os.path.abspath('./.lake/build/doc')
 
 class CustomHTTPRequestHandler(SimpleHTTPRequestHandler):
     # Avoid spurious error messages from /favicon.ico
diff --git a/sync-versions.sh b/sync-versions.sh
deleted file mode 100755
index 2e0a90b4..00000000
--- a/sync-versions.sh
+++ /dev/null
@@ -1,95 +0,0 @@
-#!/bin/bash
-
-set -e
-
-# This repository uses the library `SubVerso` to extract information
-# from the code respository and use it in the website. SubVerso is
-# compatible with every Lean release, allowing the book to use a
-# different version than the Mathlib development. The versions of the
-# library must match, however.
-#
-# The CI script '.github/workflows/check-version-consistency.yml' makes
-# sure that the versions match. If they do not, this script can be used
-# to fix the situation.
-
-echo "Extracting SubVerso version from book/lake-manifest.json..."
-if ! expected_version=$(jq -r '.packages[] | select(.name == "subverso") | .rev' book/lake-manifest.json 2>/dev/null); then
-    echo "Error: Failed to extract 'subverso' hash from book/lake-manifest.json"
-    exit 1
-fi
-
-if [[ -z "$expected_version" || "$expected_version" == "null" ]]; then
-    echo "Error: No 'subverso' package found or empty hash in book/lake-manifest.json"
-    exit 1
-fi
-
-echo "Version: $expected_version"
-
-# Check if analysis/lake-manifest.json exists
-if [[ ! -f "analysis/lake-manifest.json" ]]; then
-    echo "Error: analysis/lake-manifest.json does not exist"
-    exit 1
-fi
-
-# Get current version from analysis/lake-manifest.json
-if ! current_version=$(jq -r '.packages[] | select(.name == "subverso") | .rev' analysis/lake-manifest.json 2>/dev/null); then
-    echo "Error: Failed to extract 'subverso' hash from analysis/lake-manifest.json"
-    exit 1
-fi
-
-if [[ -z "$current_version" || "$current_version" == "null" ]]; then
-    echo "Error: No 'subverso' package found in analysis/lake-manifest.json"
-    exit 1
-fi
-
-echo "Version in analysis/lake-manifest.json: $current_version"
-
-# Check if versions already match
-if [[ "$current_version" == "$expected_version" ]]; then
-    echo "Versions already match. No changes needed."
-    exit 0
-fi
-
-
-# Use sed to replace the current hash with the expected hash
-echo "Updating subverso version in analysis/lake-manifest.json..."
-if ! sed -i.tmp "s/$current_version/$expected_version/g" analysis/lake-manifest.json; then
-    echo "Error: sed replacement failed"
-    # Restore from sed's backup if it exists
-    if [[ -f "analysis/lake-manifest.json.tmp" ]]; then
-        mv analysis/lake-manifest.json.tmp analysis/lake-manifest.json
-    fi
-    exit 1
-fi
-
-# Verify the change was made correctly
-if ! updated_version=$(jq -r '.packages[] | select(.name == "subverso") | .rev' analysis/lake-manifest.json 2>/dev/null); then
-    echo "Error: Failed to verify updated hash"
-    mv analysis/lake-manifest.json.backup analysis/lake-manifest.json
-    exit 1
-fi
-
-if [[ "$updated_version" != "$expected_version" ]]; then
-    echo "Error: Hash update verification failed"
-    echo "Expected: $expected_version"
-    echo "Found: $updated_version"
-    # Restore from sed's backup if it exists
-    if [[ -f "analysis/lake-manifest.json.tmp" ]]; then
-        mv analysis/lake-manifest.json.tmp analysis/lake-manifest.json
-    fi
-    exit 1
-fi
-
-# Count the number of changes made using sed's backup
-changes=$(diff -u analysis/lake-manifest.json.tmp analysis/lake-manifest.json | grep "^[-+]" | grep -v "^[-+][-+][-+]" | wc -l)
-if [[ $changes -ne 2 ]]; then
-    echo "Warning: Expected exactly 2 diff lines (one removal, one addition), but found $changes"
-    echo "This might indicate multiple occurrences of the hash were replaced - is there a dependency hash collision?"
-fi
-
-# Clean up sed's backup file
-rm -f analysis/lake-manifest.json.tmp
-
-echo "✓ Successfully updated subverso version in analysis/lake-manifest.json"
-echo "  From: $current_version"
-echo "  To:   $expected_version"