Build bookshelf documentation.

More consistent header levels throughout.

.envrc

@@ -0,0 +1,3 @@
+#!/usr/bin/env bash
+
+use flake

.gitignore

@@ -1,8 +1,10 @@
 # Lean
 build
+lakefile.olean
 lake-packages
 _target
 leanpkg.path
+.lake/
 
 # TeX
 *.aux
@@ -20,3 +22,9 @@ leanpkg.path
 *.synctex.gz
 *.toc
 .*.lb
+
+# direnv
+.direnv/
+
+# nix
+result

Bookshelf/Apostol.lean

@@ -1,2 +1,16 @@
 import Bookshelf.Apostol.Chapter_I_03
-import Bookshelf.Apostol.Chapter_1_11
+import Bookshelf.Apostol.Chapter_1_11
+
+/-! # Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra
+
+## Apostol, Tom M.
+
+### LaTeX
+
+Full set of [proofs and exercises](Bookshelf/Apostol.pdf).
+
+### Lean
+
+* [Chapter I.03: A Set of Axioms for the Real-Number System](Bookshelf/Apostol/Chapter_I_03.html)
+* [Chapter 1.11: Exercises](Bookshelf/Apostol/Chapter_1_11.html)
+-/

Bookshelf/Apostol/Chapter_1_11.lean

@@ -8,21 +8,21 @@ namespace Apostol.Chapter_1_11
 
 open BigOperators
 
-/-- #### Exercise 4a
+/-- ### Exercise 4a
 
 `⌊x + n⌋ = ⌊x⌋ + n` for every integer `n`.
 -/
 theorem exercise_4a (x : ℝ) (n : ℤ) : ⌊x + n⌋ = ⌊x⌋ + n :=
   Int.floor_add_int x n
 
-/-- #### Exercise 4b.1
+/-- ### Exercise 4b.1
 
 `⌊-x⌋ = -⌊x⌋` if `x` is an integer.
 -/
 theorem exercise_4b_1 (x : ℤ) : ⌊-x⌋ = -⌊x⌋ := by
   simp only [Int.floor_int, id_eq]
 
-/-- #### Exercise 4b.2
+/-- ### Exercise 4b.2
 
 `⌊-x⌋ = -⌊x⌋ - 1` otherwise.
 -/
@@ -42,7 +42,7 @@ theorem exercise_4b_2 (x : ℝ) (h : ∃ n : ℤ, x ∈ Set.Ioo ↑n (↑n + (1
   · exact (Set.mem_Ioo.mp hn).left
   · exact le_of_lt (Set.mem_Ico.mp hn').right
 
-/-- #### Exercise 4c
+/-- ### Exercise 4c
 
 `⌊x + y⌋ = ⌊x⌋ + ⌊y⌋` or `⌊x⌋ + ⌊y⌋ + 1`.
 -/
@@ -50,7 +50,7 @@ theorem exercise_4c (x y : ℝ)
   : ⌊x + y⌋ = ⌊x⌋ + ⌊y⌋ ∨ ⌊x + y⌋ = ⌊x⌋ + ⌊y⌋ + 1 := by
   have hx : x = Int.floor x + Int.fract x := Eq.symm (add_eq_of_eq_sub' rfl)
   have hy : y = Int.floor y + Int.fract y := Eq.symm (add_eq_of_eq_sub' rfl)
-  by_cases Int.fract x + Int.fract y < 1
+  by_cases h : Int.fract x + Int.fract y < 1
   · refine Or.inl ?_
     rw [Int.floor_eq_iff]
     simp only [Int.cast_add]
@@ -72,7 +72,7 @@ theorem exercise_4c (x y : ℝ)
       rw [← sub_lt_iff_lt_add', ← sub_sub, add_sub_cancel, add_sub_cancel]
       exact add_lt_add (Int.fract_lt_one x) (Int.fract_lt_one y)
 
-/-- #### Exercise 5
+/-- ### Exercise 5
 
 The formulas in Exercises 4(d) and 4(e) suggest a generalization for `⌊nx⌋`.
 State and prove such a generalization.
@@ -81,7 +81,7 @@ theorem exercise_5 (n : ℕ) (x : ℝ)
   : ⌊n * x⌋ = Finset.sum (Finset.range n) (fun i => ⌊x + i/n⌋) :=
   Real.Floor.floor_mul_eq_sum_range_floor_add_index_div n x
 
-/-- #### Exercise 4d
+/-- ### Exercise 4d
 
 `⌊2x⌋ = ⌊x⌋ + ⌊x + 1/2⌋`
 -/
@@ -94,7 +94,7 @@ theorem exercise_4d (x : ℝ)
   simp
   rw [add_comm]
 
-/-- #### Exercise 4e
+/-- ### Exercise 4e
 
 `⌊3x⌋ = ⌊x⌋ + ⌊x + 1/3⌋ + ⌊x + 2/3⌋`
 -/
@@ -108,7 +108,7 @@ theorem exercise_4e (x : ℝ)
   conv => rhs; rw [← add_rotate']; arg 2; rw [add_comm]
   rw [← add_assoc]
 
-/-- #### Exercise 7b
+/-- ### Exercise 7b
 
 If `a` and `b` are positive integers with no common factor, we have the formula
 `∑_{n=1}^{b-1} ⌊na / b⌋ = ((a - 1)(b - 1)) / 2`. When `b = 1`, the sum on the
@@ -118,14 +118,14 @@ Derive the result analytically as follows: By changing the index of summation,
 note that `Σ_{n=1}^{b-1} ⌊na / b⌋ = Σ_{n=1}^{b-1} ⌊a(b - n) / b⌋`. Now apply
 Exercises 4(a) and (b) to the bracket on the right.
 -/
-theorem exercise_7b (ha : a > 0) (hb : b > 0) (hp : Nat.coprime a b)
+theorem exercise_7b (ha : a > 0) (hb : b > 0) (hp : Nat.Coprime a b)
   : ∑ n in (Finset.range b).filter (· > 0), ⌊n * ((a : ℕ) : ℝ) / b⌋ =
       ((a - 1) * (b - 1)) / 2 := by
   sorry
 
 section
 
-/-- #### Exercise 8
+/-- ### Exercise 8
 
 Let `S` be a set of points on the real line. The *characteristic function* of
 `S` is, by definition, the function `Χ` such that `Χₛ(x) = 1` for every `x` in

Bookshelf/Apostol/Chapter_I_03.lean

@@ -1,5 +1,5 @@
 import Common.Set
-import Mathlib.Data.Real.Basic
+import Mathlib.Data.Real.Archimedean
 
 /-! # Apostol.Chapter_I_03
 
@@ -100,7 +100,7 @@ theorem is_lub_neg_set_iff_is_glb_set_neg (S : Set ℝ)
     _ = IsGreatest (lowerBounds S) (-x) := by rw [is_least_neg_set_eq_is_greatest_set_neq]
     _ = IsGLB S (-x) := rfl
 
-/-- #### Theorem I.27
+/-- ### Theorem I.27
 
 Every nonempty set `S` that is bounded below has a greatest lower bound; that
 is, there is a real number `L` such that `L = inf S`.
@@ -143,11 +143,11 @@ lemma leq_nat_abs_ceil_self (x : ℝ) : x ≤ Int.natAbs ⌈x⌉ := by
   · have h' : ((Int.natAbs ⌈x⌉) : ℝ) ≥ 0 := by simp
     calc x
       _ ≤ 0 := le_of_lt (lt_of_not_le h)
-      _ ≤ ↑(Int.natAbs ⌈x⌉) := GE.ge.le h'    
+      _ ≤ ↑(Int.natAbs ⌈x⌉) := GE.ge.le h'
 
 /-! ## The Archimedean property of the real-number system -/
 
-/-- #### Theorem I.29
+/-- ### Theorem I.29
 
 For every real `x` there exists a positive integer `n` such that `n > x`.
 -/
@@ -159,7 +159,7 @@ theorem exists_pnat_geq_self (x : ℝ) : ∃ n : ℕ+, ↑n > x := by
     _ = n := rfl
   exact ⟨n, this⟩
 
-/-- #### Theorem I.30
+/-- ### Theorem I.30
 
 If `x > 0` and if `y` is an arbitrary real number, there exists a positive
 integer `n` such that `nx > y`.
@@ -174,7 +174,7 @@ theorem exists_pnat_mul_self_geq_of_pos {x y : ℝ}
   rw [div_mul, div_self (show x ≠ 0 from LT.lt.ne' hx), div_one] at p'
   exact ⟨n, p'⟩
 
-/-- #### Theorem I.31
+/-- ### Theorem I.31
 
 If three real numbers `a`, `x`, and `y` satisfy the inequalities
 `a ≤ x ≤ a + y / n` for every integer `n ≥ 1`, then `x = a`.
@@ -243,7 +243,7 @@ theorem forall_pnat_frac_leq_self_leq_imp_eq {x y a : ℝ}
 
 /--
 Every member of a set `S` is less than or equal to some value `ub` if and only
-if `ub` is an upper bound of `S`. 
+if `ub` is an upper bound of `S`.
 -/
 lemma mem_upper_bounds_iff_forall_le {S : Set ℝ}
   : ub ∈ upperBounds S ↔ ∀ x ∈ S, x ≤ ub := by
@@ -270,7 +270,7 @@ lemma mem_imp_ge_lub {x : ℝ} (h : IsLUB S s) : x ∈ upperBounds S → x ≥ s
   intro hx
   exact h.right hx
 
-/-- #### Theorem I.32a
+/-- ### Theorem I.32a
 
 Let `h` be a given positive number and let `S` be a set of real numbers. If `S`
 has a supremum, then for some `x` in `S` we have `x > sup S - h`.
@@ -294,7 +294,7 @@ theorem sup_imp_exists_gt_sup_sub_delta {S : Set ℝ} {s h : ℝ} (hp : h > 0)
 
 /--
 Every member of a set `S` is greater than or equal to some value `lb` if and
-only if `lb` is a lower bound of `S`. 
+only if `lb` is a lower bound of `S`.
 -/
 lemma mem_lower_bounds_iff_forall_ge {S : Set ℝ}
   : lb ∈ lowerBounds S ↔ ∀ x ∈ S, x ≥ lb := by
@@ -321,7 +321,7 @@ lemma mem_imp_le_glb {x : ℝ} (h : IsGLB S s) : x ∈ lowerBounds S → x ≤ s
   intro hx
   exact h.right hx
 
-/-- #### Theorem I.32b
+/-- ### Theorem I.32b
 
 Let `h` be a given positive number and let `S` be a set of real numbers. If `S`
 has an infimum, then for some `x` in `S` we have `x < inf S + h`.
@@ -343,7 +343,7 @@ theorem inf_imp_exists_lt_inf_add_delta {S : Set ℝ} {s h : ℝ} (hp : h > 0)
     exact le_of_not_gt (not_and.mp (nb x) hx)
   rwa [← mem_lower_bounds_iff_forall_ge] at nb'
 
-/-- #### Theorem I.33a (Additive Property)
+/-- ### Theorem I.33a (Additive Property)
 
 Given nonempty subsets `A` and `B` of `ℝ`, let `C` denote the set
 `C = {a + b : a ∈ A, b ∈ B}`. If each of `A` and `B` has a supremum, then `C`
@@ -393,7 +393,7 @@ theorem sup_minkowski_sum_eq_sup_add_sup (A B : Set ℝ) (a b : ℝ)
       _ ≤ a' + b' + 1 / n := le_of_lt hab'
       _ ≤ c + 1 / n := add_le_add_right hc' (1 / n)
 
-/-- #### Theorem I.33b (Additive Property)
+/-- ### Theorem I.33b (Additive Property)
 
 Given nonempty subsets `A` and `B` of `ℝ`, let `C` denote the set
 `C = {a + b : a ∈ A, b ∈ B}`. If each of `A` and `B` has an infimum, then `C`
@@ -443,7 +443,7 @@ theorem inf_minkowski_sum_eq_inf_add_inf (A B : Set ℝ)
       _ ≤ a + b := le_of_lt hab'
   · exact hc.right hlb
 
-/-- #### Theorem I.34
+/-- ### Theorem I.34
 
 Given two nonempty subsets `S` and `T` of `ℝ` such that `s ≤ t` for every `s` in
 `S` and every `t` in `T`. Then `S` has a supremum, and `T` has an infimum, and
@@ -489,7 +489,7 @@ theorem forall_mem_le_forall_mem_imp_sup_le_inf (S T : Set ℝ)
     _ < x := hx.right
   simp at this
 
-/-- #### Exercise 1
+/-- ### Exercise 1
 
 If `x` and `y` are arbitrary real numbers with `x < y`, prove that there is at
 least one real `z` satisfying `x < z < y`.
@@ -506,7 +506,7 @@ theorem exercise_1 (x y : ℝ) (h : x < y) : ∃ z, x < z ∧ z < y := by
       _ < x + z := (add_lt_add_iff_left x).mpr hz'
       _ = y := hz.right
 
-/-- #### Exercise 2
+/-- ### Exercise 2
 
 If `x` is an arbitrary real number, prove that there are integers `m` and `n`
 such that `m < x < n`.
@@ -514,7 +514,7 @@ such that `m < x < n`.
 theorem exercise_2 (x : ℝ) : ∃ m n : ℝ, m < x ∧ x < n := by
   refine ⟨x - 1, ⟨x + 1, ⟨?_, ?_⟩⟩⟩ <;> norm_num
 
-/-- #### Exercise 3
+/-- ### Exercise 3
 
 If `x > 0`, prove that there is a positive integer `n` such that `1 / n < x`.
 -/
@@ -525,7 +525,7 @@ theorem exercise_3 (x : ℝ) (h : x > 0) : ∃ n : ℕ+, 1 / n < x := by
   conv at hr => arg 2; rw [mul_comm, ← mul_assoc]; simp
   rwa [one_mul] at hr
 
-/-- #### Exercise 4
+/-- ### Exercise 4
 
 If `x` is an arbitrary real number, prove that there is exactly one integer `n`
 which satisfies the inequalities `n ≤ x < n + 1`. This `n` is called the
@@ -540,7 +540,7 @@ theorem exercise_4 (x : ℝ) : ∃! n : ℤ, n ≤ x ∧ x < n + 1 := by
     rw [← Int.floor_eq_iff] at hy
     exact Eq.symm hy
 
-/-- #### Exercise 5
+/-- ### Exercise 5
 
 If `x` is an arbitrary real number, prove that there is exactly one integer `n`
 which satisfies `x ≤ n < x + 1`.
@@ -559,7 +559,7 @@ theorem exercise_5 (x : ℝ) : ∃! n : ℤ, x ≤ n ∧ n < x + 1 := by
       rwa [add_sub_cancel] at this
     · exact hy.left
 
-/-! #### Exercise 6
+/-! ### Exercise 6
 
 If `x` and `y` are arbitrary real numbers, `x < y`, prove that there exists at
 least one rational number `r` satisfying `x < r < y`, and hence infinitely many.
@@ -569,7 +569,7 @@ in the real-number system.
 ###### TODO
 -/
 
-/-! #### Exercise 7
+/-! ### Exercise 7
 
 If `x` is rational, `x ≠ 0`, and `y` irrational, prove that `x + y`, `x - y`,
 `xy`, `x / y`, and `y / x` are all irrational.
@@ -577,14 +577,14 @@ If `x` is rational, `x ≠ 0`, and `y` irrational, prove that `x + y`, `x - y`,
 ###### TODO
 -/
 
-/-! #### Exercise 8
+/-! ### Exercise 8
 
 Is the sum or product of two irrational numbers always irrational?
 
 ###### TODO
 -/
 
-/-! #### Exercise 9
+/-! ### Exercise 9
 
 If `x` and `y` are arbitrary real numbers, `x < y`, prove that there exists at
 least one irrational number `z` satisfying `x < z < y`, and hence infinitely
@@ -593,7 +593,7 @@ many.
 ###### TODO
 -/
 
-/-! #### Exercise 10
+/-! ### Exercise 10
 
 An integer `n` is called *even* if `n = 2m` for some integer `m`, and *odd* if
 `n + 1` is even. Prove the following statements:
@@ -618,7 +618,7 @@ def isEven (n : ℤ) := ∃ m : ℤ, n = 2 * m
 
 def isOdd (n : ℤ) := isEven (n + 1)
 
-/-! #### Exercise 11
+/-! ### Exercise 11
 
 Prove that there is no rational number whose square is `2`.
 
@@ -629,7 +629,7 @@ contradiction.]
 ###### TODO
 -/
 
-/-! #### Exercise 12
+/-! ### Exercise 12
 
 The Archimedean property of the real-number system was deduced as a consequence
 of the least-upper-bound axiom. Prove that the set of rational numbers satisfies

Bookshelf/Avigad.lean

@@ -3,4 +3,18 @@ import Bookshelf.Avigad.Chapter_3
 import Bookshelf.Avigad.Chapter_4
 import Bookshelf.Avigad.Chapter_5
 import Bookshelf.Avigad.Chapter_7
-import Bookshelf.Avigad.Chapter_8
+import Bookshelf.Avigad.Chapter_8
+
+/-! # Theorem Proving in Lean
+
+## Avigad, Jeremy.
+
+### Lean
+
+* [Chapter 2: Dependent Type Theory](Bookshelf/Avigad/Chapter_2.html)
+* [Chapter 3: Propositions and Proofs](Bookshelf/Avigad/Chapter_3.html)
+* [Chapter 4: Quantifiers and Equality](Bookshelf/Avigad/Chapter_4.html)
+* [Chapter 5: Tactics](Bookshelf/Avigad/Chapter_5.html)
+* [Chapter 7: Inductive Types](Bookshelf/Avigad/Chapter_7.html)
+* [Chapter 8: Induction and Recursion](Bookshelf/Avigad/Chapter_8.html)
+-/

Bookshelf/Avigad/Chapter_2.lean

@@ -3,7 +3,7 @@
 Dependent Type Theory
 -/
 
-/-! #### Exercise 1
+/-! ### Exercise 1
 
 Define the function `Do_Twice`, as described in Section 2.4.
 -/
@@ -20,7 +20,7 @@ def doTwiceTwice (f : (Nat → Nat) → (Nat → Nat)) (x : Nat → Nat) := f (f
 
 end ex1
 
-/-! #### Exercise 2
+/-! ### Exercise 2
 
 Define the functions `curry` and `uncurry`, as described in Section 2.4.
 -/
@@ -35,7 +35,7 @@ def uncurry (f : α → β → γ) : (α × β → γ) :=
 
 end ex2
 
-/-! #### Exercise 3
+/-! ### Exercise 3
 
 Above, we used the example `vec α n` for vectors of elements of type `α` of
 length `n`. Declare a constant `vec_add` that could represent a function that
@@ -70,7 +70,7 @@ variable (c d : vec Prop 2)
 
 end ex3
 
-/-! #### Exercise 4
+/-! ### Exercise 4
 
 Similarly, declare a constant `matrix` so that `matrix α m n` could represent
 the type of `m` by `n` matrices. Declare some constants to represent functions
@@ -106,4 +106,4 @@ variable (d : ex3.vec Prop 3)
 
 end ex4
 
-end Avigad.Chapter2
+end Avigad.Chapter2

Bookshelf/Avigad/Chapter_3.lean

@@ -3,7 +3,7 @@
 Propositions and Proofs
 -/
 
-/-! #### Exercise 1
+/-! ### Exercise 1
 
 Prove the following identities.
 -/
@@ -104,7 +104,7 @@ theorem imp_imp_not_imp_not : (p → q) → (¬q → ¬p) :=
 
 end ex1
 
-/-! #### Exercise 2
+/-! ### Exercise 2
 
 Prove the following identities. These require classical reasoning.
 -/
@@ -150,7 +150,7 @@ theorem imp_imp_imp : (((p → q) → p) → p) :=
 
 end ex2
 
-/-! #### Exercise 3
+/-! ### Exercise 3
 
 Prove `¬(p ↔ ¬p)` without using classical logic.
 -/
@@ -164,4 +164,4 @@ theorem iff_not_self (hp : p) : ¬(p ↔ ¬p) :=
 
 end ex3
 
-end Avigad.Chapter3
+end Avigad.Chapter3

Bookshelf/Avigad/Chapter_4.lean

@@ -40,7 +40,7 @@ theorem forall_or_distrib
 
 end ex1
 
-/-! #### Exercise 2
+/-! ### Exercise 2
 
 It is often possible to bring a component of a formula outside a universal
 quantifier, when it does not depend on the quantified variable. Try proving
@@ -78,7 +78,7 @@ theorem forall_swap : (∀ x, r → p x) ↔ (r → ∀ x, p x) :=
 
 end ex2
 
-/-! #### Exercise 3
+/-! ### Exercise 3
 
 Consider the "barber paradox," that is, the claim that in a certain town there
 is a (male) barber that shaves all and only the men who do not shave themselves.
@@ -101,7 +101,7 @@ theorem barber_paradox (h : ∀ x : men, shaves barber x ↔ ¬shaves x x) : Fal
 
 end ex3
 
-/-! #### Exercise 4
+/-! ### Exercise 4
 
 Remember that, without any parameters, an expression of type `Prop` is just an
 assertion. Fill in the definitions of `prime` and `Fermat_prime` below, and
@@ -143,7 +143,7 @@ def Fermat'sLastTheorem : Prop :=
 
 end ex4
 
-/-! #### Exercise 5
+/-! ### Exercise 5
 
 Prove as many of the identities listed in Section 4.4 as you can.
 -/
@@ -228,7 +228,7 @@ theorem exists_self_iff_self_exists (a : α) : (∃ x, r → p x) ↔ (r → ∃
 
 end ex5
 
-/-! #### Exercise 6
+/-! ### Exercise 6
 
 Give a calculational proof of the theorem `log_mul` below.
 -/
@@ -258,4 +258,4 @@ theorem log_mul {x y : Float} (hx : x > 0) (hy : y > 0) :
 
 end ex6
 
-end Avigad.Chapter4
+end Avigad.Chapter4

Bookshelf/Avigad/Chapter_5.lean

@@ -13,7 +13,7 @@ namespace Avigad.Chapter5
 
 namespace ex1
 
-/-! ##### Exercises 3.1 -/
+/-! #### Exercises 3.1 -/
 
 section ex3_1
 
@@ -154,7 +154,7 @@ theorem imp_imp_not_imp_not : (p → q) → (¬q → ¬p) := by
 
 end ex3_1
 
-/-! ##### Exercises 3.2 -/
+/-! #### Exercises 3.2 -/
 
 section ex3_2
 
@@ -223,7 +223,7 @@ theorem imp_imp_imp : (((p → q) → p) → p) := by
 
 end ex3_2
 
-/-! ##### Exercises 3.3 -/
+/-! #### Exercises 3.3 -/
 
 section ex3_3
 
@@ -235,7 +235,7 @@ theorem iff_not_self (hp : p) : ¬(p ↔ ¬p) := by
 
 end ex3_3
 
-/-! ##### Exercises 4.1 -/
+/-! #### Exercises 4.1 -/
 
 section ex4_1
 
@@ -264,7 +264,7 @@ theorem forall_or_distrib : (∀ x, p x) ∨ (∀ x, q x) → ∀ x, p x ∨ q x
 
 end ex4_1
 
-/-! ##### Exercises 4.2 -/
+/-! #### Exercises 4.2 -/
 
 section ex4_2
 
@@ -316,7 +316,7 @@ theorem forall_swap : (∀ x, r → p x) ↔ (r → ∀ x, p x) := by
 
 end ex4_2
 
-/-! ##### Exercises 4.3 -/
+/-! #### Exercises 4.3 -/
 
 section ex4_3
 
@@ -336,7 +336,7 @@ theorem barber_paradox (h : ∀ x : men, shaves barber x ↔ ¬ shaves x x)
 
 end ex4_3
 
-/-! ##### Exercises 4.5 -/
+/-! #### Exercises 4.5 -/
 
 section ex4_5
 
@@ -448,7 +448,7 @@ end ex4_5
 
 end ex1
 
-/-! #### Exercise 2
+/-! ### Exercise 2
 
 Use tactic combinators to obtain a one line proof of the following:
 -/
@@ -461,4 +461,4 @@ theorem or_and_or_and_or (p q r : Prop) (hp : p)
 
 end ex2
 
-end Avigad.Chapter5
+end Avigad.Chapter5

Bookshelf/Avigad/Chapter_7.lean

@@ -5,7 +5,7 @@ Inductive Types
 
 namespace Avigad.Chapter7
 
-/-! #### Exercise 1
+/-! ### Exercise 1
 
 Try defining other operations on the natural numbers, such as multiplication,
 the predecessor function (with `pred 0 = 0`), truncated subtraction (with
@@ -77,7 +77,7 @@ end Nat
 
 end ex1
 
-/-! #### Exercise 2
+/-! ### Exercise 2
 
 Define some operations on lists, like a `length` function or the `reverse`
 function. Prove some properties, such as the following:
@@ -178,7 +178,7 @@ theorem reverse_reverse (t : List α)
 
 end ex2
 
-/-! #### Exercise 3
+/-! ### Exercise 3
 
 Define an inductive data type consisting of terms built up from the following
 constructors:
@@ -217,4 +217,4 @@ def eval_foo : Foo → List Nat → Nat
 
 end ex3
 
-end Avigad.Chapter7
+end Avigad.Chapter7

Bookshelf/Avigad/Chapter_8.lean

@@ -5,7 +5,7 @@ Induction and Recursion
 
 namespace Avigad.Chapter8
 
-/-! #### Exercise 1
+/-! ### Exercise 1
 
 Open a namespace `Hidden` to avoid naming conflicts, and use the equation
 compiler to define addition, multiplication, and exponentiation on the natural
@@ -29,7 +29,7 @@ def exp : Nat → Nat → Nat
 
 end ex1
 
-/-! #### Exercise 2
+/-! ### Exercise 2
 
 Similarly, use the equation compiler to define some basic operations on lists
 (like the reverse function) and prove theorems about lists by induction (such as
@@ -48,7 +48,7 @@ def reverse : List α → List α
 
 end ex2
 
-/-! #### Exercise 3
+/-! ### Exercise 3
 
 Define your own function to carry out course-of-value recursion on the natural
 numbers. Similarly, see if you can figure out how to define `WellFounded.fix` on
@@ -86,7 +86,7 @@ noncomputable def brecOn {motive : Nat → Sort u}
 
 end ex3
 
-/-! #### Exercise 4
+/-! ### Exercise 4
 
 Following the examples in Section Dependent Pattern Matching, define a function
 that will append two vectors. This is tricky; you will have to define an
@@ -113,7 +113,7 @@ end Vector
 
 end ex4
 
-/-! #### Exercise 5
+/-! ### Exercise 5
 
 Consider the following type of arithmetic expressions.
 -/
@@ -149,7 +149,7 @@ def sampleVal : Nat → Nat
 -- Try it out. You should get 47 here.
 #eval eval sampleVal sampleExpr
 
-/-! ##### Constant Fusion
+/-! ### Constant Fusion
 
 Implement "constant fusion," a procedure that simplifies subterms like `5 + 7
 to `12`. Using the auxiliary function `simpConst`, define a function "fuse": to
@@ -189,7 +189,7 @@ theorem simpConst_eq (v : Nat → Nat)
   | times _ (var     _)
   | times _ (plus  _ _)
   | times _ (times _ _) => simp only
-  
+
 
 theorem fuse_eq (v : Nat → Nat)
   : ∀ e : Expr, eval v (fuse e) = eval v e := by
@@ -206,4 +206,4 @@ theorem fuse_eq (v : Nat → Nat)
 
 end ex5
 
-end Avigad.Chapter8
+end Avigad.Chapter8

Bookshelf/Enderton/Logic.lean

@@ -1 +1,14 @@
-import Bookshelf.Enderton.Logic.Chapter_1
+import Bookshelf.Enderton.Logic.Chapter_1
+
+/-! # A Mathematical Introduction to Logic
+
+## Enderton, Herbert B.
+
+### LaTeX
+
+Full set of [proofs and exercises](Bookshelf/Enderton/Logic.pdf).
+
+### Lean
+
+* [Chapter 1: Sentential Logic](Bookshelf/Enderton/Logic/Chapter_1.html)
+-/

Bookshelf/Enderton/Logic/Chapter_1.lean

@@ -131,7 +131,7 @@ lemma no_neg_sentential_count_eq_binary_count {φ : Wff} (h : ¬φ.hasNotSymbol)
     unfold sententialSymbolCount binarySymbolCount
     rw [ih₁ h.left, ih₂ h.right]
 
-/-- #### Parentheses Count
+/-- ### Parentheses Count
 
 Let `φ` be a well-formed formula and `c` be the number of places at which a
 sentential connective symbol exists. Then there is `2c` parentheses in `φ`.
@@ -180,7 +180,7 @@ theorem length_eq_sum_symbol_count (φ : Wff)
 
 end Wff
 
-/-! #### Exercise 1.1.2
+/-! ### Exercise 1.1.2
 
 Show that there are no wffs of length `2`, `3`, or `6`, but that any other
 positive length is possible.
@@ -296,7 +296,7 @@ theorem exercise_1_1_2_ii (n : ℕ) (hn : n ≠ 2 ∧ n ≠ 3 ∧ n ≠ 6)
 
 end Exercise_1_1_2
 
-/-- #### Exercise 1.1.3
+/-- ### Exercise 1.1.3
 
 Let `α` be a wff; let `c` be the number of places at which binary connective
 symbols (`∧`, `∨`, `→`, `↔`) occur in `α`; let `s` be the number of places at
@@ -320,7 +320,7 @@ theorem exercise_1_1_3 (φ : Wff)
     rw [ih₁, ih₂]
     ring
 
-/-- #### Exercise 1.1.5 (a)
+/-- ### Exercise 1.1.5 (a)
 
 Suppose that `α` is a wff not containing the negation symbol `¬`. Show that the
 length of `α` (i.e., the number of symbols in the string) is odd.
@@ -355,7 +355,7 @@ theorem exercise_1_1_5a (α : Wff) (hα : ¬α.hasNotSymbol)
     rw [hk₁, hk₂]
     ring
 
-/-- #### Exercise 1.1.5 (b)
+/-- ### Exercise 1.1.5 (b)
 
 Suppose that `α` is a wff not containing the negation symbol `¬`. Show that more
 than a quarter of the symbols are sentence symbols.
@@ -390,7 +390,7 @@ theorem exercise_1_1_5b (α : Wff) (hα : ¬α.hasNotSymbol)
   ]
   exact inv_lt_one (by norm_num)
 
-/-! #### Exercise 1.2.1
+/-! ### Exercise 1.2.1
 
 Show that neither of the following two formulas tautologically implies the
 other:
@@ -430,7 +430,7 @@ theorem exercise_1_2_2a (P Q : Prop)
   : (((P → Q) → P) → P) := by
   tauto
 
-/-! #### Exercise 1.2.2 (b)
+/-! ### Exercise 1.2.2 (b)
 
 Define `σₖ` recursively as follows: `σ₀ = (P → Q)` and `σₖ₊₁ = (σₖ → P)`. For
 which values of `k` is `σₖ` a tautology? (Part (a) corresponds to `k = 2`.)
@@ -475,18 +475,18 @@ theorem exercise_1_2_2b_iii {k : ℕ} (h : Odd k)
       have ⟨r, hr⟩ := h
       refine ⟨r, hr, ?_⟩
       by_contra nr
-      have : r = 0 := Nat.eq_zero_of_nonpos r nr
+      have : r = 0 := Nat.eq_zero_of_not_pos nr
       rw [this] at hr
       simp only [mul_zero, zero_add] at hr
       exact absurd hr hk
     unfold σ
     rw [hn₁]
-    simp only [Nat.add_eq, add_zero, not_forall, exists_prop, and_true]
+    simp only [Nat.add_eq, add_zero, imp_false, not_not]
     exact exercise_1_2_2b_i False Q hn₂
 
 end Exercise_1_2_2
 
-/-- #### Exercise 1.2.3 (a)
+/-- ### Exercise 1.2.3 (a)
 
 Determine whether or not `((P → Q)) ∨ (Q → P)` is a tautology.
 -/
@@ -494,7 +494,7 @@ theorem exercise_1_2_3a (P Q : Prop)
   : ((P → Q) ∨ (Q → P)) := by
   tauto
 
-/-- #### Exercise 1.2.3 (b)
+/-- ### Exercise 1.2.3 (b)
 
 Determine whether or not `((P ∧ Q) → R))` tautologically implies
 `((P → R) ∨ (Q → R))`.
@@ -503,7 +503,7 @@ theorem exercise_1_2_3b (P Q R : Prop)
   : ((P ∧ Q) → R) ↔ ((P → R) ∨ (Q → R)) := by
   tauto
 
-/-! #### Exercise 1.2.5
+/-! ### Exercise 1.2.5
 
 Prove or refute each of the following assertions:
 
@@ -519,7 +519,7 @@ theorem exercise_1_2_6b
   : (False ∨ True) ∧ ¬ False := by
   simp
 
-/-! #### Exercise 1.2.15
+/-! ### Exercise 1.2.15
 
 Of the following three formulas, which tautologically implies which?
 (a) `(A ↔ B)`

Bookshelf/Enderton/Set.lean

@@ -4,4 +4,21 @@ import Bookshelf.Enderton.Set.Chapter_3
 import Bookshelf.Enderton.Set.Chapter_4
 import Bookshelf.Enderton.Set.Chapter_6
 import Bookshelf.Enderton.Set.OrderedPair
-import Bookshelf.Enderton.Set.Relation
+import Bookshelf.Enderton.Set.Relation
+
+/-! # Elements of Set Theory
+
+## Enderton, Herbert B.
+
+### LaTeX
+
+Full set of [proofs and exercises](Bookshelf/Enderton/Set.pdf).
+
+### Lean
+
+* [Chapter 1: Introduction](Bookshelf/Enderton/Set/Chapter_1.html)
+* [Chapter 2: Axioms and Operations](Bookshelf/Enderton/Set/Chapter_2.html)
+* [Chapter 3: Relations and Functions](Bookshelf/Enderton/Set/Chapter_3.html)
+* [Chapter 4: Natural Numbers](Bookshelf/Enderton/Set/Chapter_4.html)
+* [Chapter 6: Cardinal Numbers and the Axiom of Choice](Bookshelf/Enderton/Set/Chapter_6.html)
+-/

Bookshelf/Enderton/Set.tex

@@ -64,6 +64,47 @@
   A \textbf{binary operation} on a set $A$ is a \nameref{ref:function} from
     $A \times A$ into $A$.
 
+\section{\defined{Cardinal Arithmetic}}%
+\hyperlabel{sec:cardinal-arithmetic}
+
+  Let $\kappa$ and $\lambda$ be any cardinal numbers.
+  \begin{enumerate}[(a)]
+    \item $\kappa + \lambda = \card{(K \cup L)}$, where $K$ and $L$ are any
+      disjoint sets of cardinality $\kappa$ and $\lambda$, respectively.
+    \item $\kappa \cdot \lambda = \card{(K \times L)}$, where $K$ and $L$ are
+      any sets of cardinality $\kappa$ and $\lambda$, respectively.
+    \item $\kappa^\lambda = \card{(^L{K})}$, where $K$ and $L$ are any sets of
+      cardinality $\kappa$ and $\lambda$, respectively.
+  \end{enumerate}
+
+  \lean{Mathlib/SetTheory/Cardinal/Basic}
+    {Cardinal.add\_def}
+
+  \lean{Mathlib/SetTheory/Cardinal/Basic}
+    {Cardinal.mul\_def}
+
+  \lean{Mathlib/SetTheory/Cardinal/Basic}
+    {Cardinal.power\_def}
+
+\section{\defined{Cardinal Number}}%
+\hyperlabel{ref:cardinal-number}
+
+  For any set $C$, the \textbf{cardinal number} of set $C$ is denoted as
+    $\card{C}$.
+  Furthermore,
+    \begin{enumerate}[(a)]
+      \item For any sets $A$ and $B$,
+        $$\card{A} = \card{B} \quad\text{iff}\quad A \equin B.$$
+      \item For a finite set $A$, $\card{A}$ is the \nameref{ref:natural-number}
+        $n$ for which $A \equin n$.
+    \end{enumerate}
+
+  \lean{Mathlib/Data/Finset/Card}
+    {Finset.card}
+
+  \lean{Mathlib/SetTheory/Cardinal/Basic}
+    {Cardinal}
+
 \section{\defined{Cartesian Product}}%
 \hyperlabel{ref:cartesian-product}
 
@@ -77,19 +118,6 @@
 
   \lean{Mathlib/Data/Set/Prod}{Set.prod}
 
-\section{\defined{Cardinal Arithmetic}}%
-\hyperlabel{sec:cardinal-arithmetic}
-
-  Let $\kappa$ and $\lambda$ be any cardinal numbers.
-  \begin{enumerate}[(a)]
-    \item $\kappa + \lambda = \card{(K \cup L)}$, where $K$ and $L$ are any
-      disjoint sets of cardinality $\kappa$ and $\lambda$, respectively.
-    \item $\kappa \cdot \lambda = \card{(K \times L)}$, where $K$ and $L$ are
-      any sets of cardinality $\kappa$ and $\lambda$, respectively.
-    \item $\kappa^\lambda = \card{^L{K}}$, where $K$ and $L$ are any sets of
-      cardinality $\kappa$ and $\lambda$, respectively.
-  \end{enumerate}
-
 \section{\defined{Compatible}}%
 \hyperlabel{ref:compatible}
 
@@ -142,9 +170,8 @@
 \section{\defined{Equinumerous}}%
 \hyperlabel{ref:equinumerous}
 
-  A set $A$ is \textbf{equinumerous} to a set $B$ (written
-    $\equinumerous{A}{B}$) if and only if there is a one-to-one
-    \nameref{ref:function} from $A$ onto $B$.
+  A set $A$ is \textbf{equinumerous} to a set $B$ (written $A \equin B$) if and
+    only if there is a one-to-one \nameref{ref:function} from $A$ onto $B$.
   In other words, there exists a one-to-one correspondence between $A$ and $B$.
 
   \lean*{Mathlib/Init/Function}
@@ -394,6 +421,17 @@
   \lean{Init/Prelude}
     {Mul.mul}
 
+\section{\defined{Natural Map}}%
+\hyperlabel{ref:natural-map}
+
+  Let $R$ be an \nameref{ref:equivalence-relation} on $A$.
+  Then the \textbf{natural map} (or \textbf{canonical map})
+    $\phi \colon A \rightarrow A / R$ is defined as $$\phi(x) = [x]_R$$ for
+    $x \in A$.
+
+  \lean*{Init/Core}
+    {Quotient.lift}
+
 \section{\defined{Natural Number}}%
 \hyperlabel{ref:natural-number}
 
@@ -1876,7 +1914,7 @@
     We proceed by contradiction.
     Suppose there existed a set $A$ consisting of every singleton.
     Then the \nameref{ref:union-axiom} suggests $\bigcup A$ is a set.
-    But this set is precisely the class of all sets, which is \textit{not} a
+    But this "set" is precisely the class of all sets, which is \textit{not} a
       set.
     Thus our original assumption was incorrect.
     That is, there is no set to which every singleton belongs.
@@ -3045,6 +3083,9 @@
   \code{Bookshelf/Enderton/Set/Relation}
     {Set.Relation.one\_to\_one\_comp\_is\_one\_to\_one}
 
+  \lean{Mathlib/Data/Set/Function}
+    {Set.InjOn.comp}
+
   \begin{proof}
     Let $F \colon B \rightarrow C$ and $G \colon A \rightarrow B$ be
       one-to-one \nameref{ref:function}s from sets $A$, $B$, and $C$.
@@ -3089,91 +3130,93 @@
       \end{align*}
   \end{proof}
 
-\subsection{\verified{Theorem 3J}}%
-\hyperlabel{sub:theorem-3j}
+\subsection{\verified{Theorem 3J (a)}}%
+\hyperlabel{sub:theorem-3j-a}
 
-  \begin{theorem}[3J]
+  \begin{theorem}[3J(a)]
     Assume that $F \colon A \rightarrow B$, and that $A$ is nonempty.
-    \begin{enumerate}[(a)]
-      \item There exists a function $G \colon B \rightarrow A$
-        (a "left inverse") such that $G \circ F$ is the identity function $I_A$
-        on $A$ iff $F$ is one-to-one.
-      \item There exists a function $H \colon B \rightarrow A$
-        (a "right inverse") such that $F \circ H$ is the identity function $I_B$
-        on $B$ iff $F$ maps $A$ \textit{onto} $B$.
-    \end{enumerate}
+    There exists a function $G \colon B \rightarrow A$ (a "left inverse") such
+      that $G \circ F$ is the identity function $I_A$ on $A$ iff $F$ is
+      one-to-one.
   \end{theorem}
 
   \code{Bookshelf/Enderton/Set/Chapter\_3}
     {Enderton.Set.Chapter\_3.theorem\_3j\_a}
 
+  \begin{proof}
+
+    Let $F$ be a \nameref{ref:function} from nonempty set $A$ to set $B$.
+
+    \subparagraph{($\Rightarrow$)}%
+
+      Let $G \colon B \rightarrow A$ such that $G \circ F = I_A$.
+      All that remains is to prove $F$ is single-rooted.
+      Let $y \in \ran{F}$.
+      By definition of the \nameref{ref:range} of a function, there exists
+        some $x_1$ such that $\tuple{x_1, y} \in F$.
+      Suppose there exists a set $x_2$ such that $\tuple{x_2, y} \in F$.
+      By hypothesis, $G(F(x_1)) = G(F(x_2))$ implies $I_A(x_1) = I_A(x_2)$.
+      Thus $x_1 = x_2$.
+      Therefore $F$ must be single-rooted.
+
+    \subparagraph{($\Leftarrow$)}%
+
+      Let $F$ be one-to-one.
+      Since $A$ is nonempty, there exists some $a \in A$.
+      Let $G \colon B \rightarrow A$ be given by
+        $$G(y) = \begin{cases}
+          F^{-1}(y) & \text{if } y \in \ran{F} \\
+          a & \text{otherwise}.
+        \end{cases}$$
+      $G$ is a function by virtue of \nameref{sub:one-to-one-inverse} and
+        choice of mapping for all values $y \not\in \ran{F}$.
+      Furthermore, for all $x \in A$, $F(x) \in \ran{F}$.
+      Thus $(G \circ F)(x) = G(F(x)) = F^{-1}(F(x)) = x$ by
+        \nameref{sub:theorem-3g}.
+
+  \end{proof}
+
+\subsection{\unverified{Theorem 3J (b)}}%
+\hyperlabel{sub:theorem-3j-b}
+
+  \begin{theorem}[3J(b)]
+    Assume that $F \colon A \rightarrow B$, and that $A$ is nonempty.
+    There exists a function $H \colon B \rightarrow A$ (a "right inverse") such
+      that $F \circ H$ is the identity function $I_B$ on $B$ iff $F$ maps $A$
+      \textit{onto} $B$.
+  \end{theorem}
+
   \code{Bookshelf/Enderton/Set/Chapter\_3}
     {Enderton.Set.Chapter\_3.theorem\_3j\_b}
 
   \begin{proof}
+
     Let $F$ be a \nameref{ref:function} from nonempty set $A$ to set $B$.
 
-    \paragraph{(a)}%
+    \subparagraph{($\Rightarrow$)}%
 
-      We prove there exists a function $G \colon B \rightarrow A$ such that
-        $G \circ F = I_A$ if and only if $F$ is one-to-one.
+      Suppose $H \colon B \rightarrow A$ such that $F \circ H = I_A$.
+      All that remains is to prove $\ran{F} = B$.
+      Note that $\ran{F} \subseteq B$ by hypothesis.
+      Let $y \in B$.
+      But $F(H(y)) = y$ meaning $y \in \ran{F}$.
+      Thus $B \subseteq \ran{F}$.
+      Since $\ran{F} \subseteq B$ and $B \subseteq \ran{F}$, $\ran{F} = B$.
 
-      \subparagraph{($\Rightarrow$)}%
+    \subparagraph{($\Leftarrow$)}%
 
-        Let $G \colon B \rightarrow A$ such that $G \circ F = I_A$.
-        All that remains is to prove $F$ is single-rooted.
-        Let $y \in \ran{F}$.
-        By definition of the \nameref{ref:range} of a function, there exists
-          some $x_1$ such that $\tuple{x_1, y} \in F$.
-        Suppose there exists a set $x_2$ such that $\tuple{x_2, y} \in F$.
-        By hypothesis, $G(F(x_1)) = G(F(x_2))$ implies $I_A(x_1) = I_A(x_2)$.
-        Thus $x_1 = x_2$.
-        Therefore $F$ must be single-rooted.
-
-      \subparagraph{($\Leftarrow$)}%
-
-        Let $F$ be one-to-one.
-        Since $A$ is nonempty, there exists some $a \in A$.
-        Let $G \colon B \rightarrow A$ be given by
-          $$G(y) = \begin{cases}
-            F^{-1}(y) & \text{if } y \in \ran{F} \\
-            a & \text{otherwise}.
-          \end{cases}$$
-        $G$ is a function by virtue of \nameref{sub:one-to-one-inverse} and
-          choice of mapping for all values $y \not\in \ran{F}$.
-        Furthermore, for all $x \in A$, $F(x) \in \ran{F}$.
-        Thus $(G \circ F)(x) = G(F(x)) = F^{-1}(F(x)) = x$ by
-          \nameref{sub:theorem-3g}.
-
-    \paragraph{(b)}%
-
-      We prove there exists a function $H \colon B \rightarrow A$ such that
-        $F \circ H = I_A$ if and only if $F$ maps $A$ onto $B$.
-
-      \subparagraph{($\Rightarrow$)}%
-
-        Suppose $H \colon B \rightarrow A$ such that $F \circ H = I_A$.
-        All that remains is to prove $\ran{F} = B$.
-        Note that $\ran{F} \subseteq B$ by hypothesis.
-        Let $y \in B$.
-        But $F(H(y)) = y$ meaning $y \in \ran{F}$.
-        Thus $B \subseteq \ran{F}$.
-        Since $\ran{F} \subseteq B$ and $B \subseteq \ran{F}$, $\ran{F} = B$.
-
-      \subparagraph{($\Leftarrow$)}%
-
-        Suppose $F$ maps $A$ \textit{onto} $B$.
-        By definition of maps onto, $\ran{F} = B$.
-        Then for all $y \in B$, there exists some $x \in A$ such that
-          $\tuple{x, y} \in F$.
-        Notice though that $F^{-1}[\{y\}]$ may not be a singleton set.
-        Then there is no obvious way to \textit{choose} an element from each
-          preimage to form a function.
-        By the \nameref{ref:axiom-of-choice-1}, there exists a function
-          $H \subseteq F^{-1}$ such that $\dom{H} = \dom{F^{-1}} = B$.
-        For all $y \in B$, $\tuple{y, H(y)} \in H \subseteq F^{-1}$
-          meaning $\tuple{H(y), y} \in F$.
-        Thus $F(H(y)) = y$ as expected.
+      Suppose $F$ maps $A$ \textit{onto} $B$.
+      By definition of maps onto, $\ran{F} = B$.
+      Then for all $y \in B$, there exists some $x \in A$ such that
+        $\tuple{x, y} \in F$.
+      Notice though that $F^{-1}[\{y\}]$ may not be a singleton set.
+      Then there is no obvious way to \textit{choose} an element from each
+        preimage to form a function.
+      By the \nameref{ref:axiom-of-choice-1}, there exists a function
+        $H \subseteq F^{-1}$ such that $\dom{H} = \dom{F^{-1}} = B$.
+      For all $y \in B$, $\tuple{y, H(y)} \in H \subseteq F^{-1}$
+        meaning $\tuple{H(y), y} \in F$.
+      Thus $F(H(y)) = y$ as expected.
 
   \end{proof}
 
@@ -3188,9 +3231,9 @@
   \begin{proof}
     By definition, a one-to-one correspondence $f$ between sets $A$ and $B$ must
       be both one-to-one and onto.
-    By \nameref{sub:theorem-3j}, $f$ is one-to-one if and only if it has a left
-      inverse.
-    The same theorem states that $f$ is onto $B$ if and only if it has a right
+    By \nameref{sub:theorem-3j-a}, $f$ is one-to-one if and only if it has a
+      left inverse.
+    By \nameref{sub:theorem-3j-b}, $f$ is onto $B$ if and only if it has a right
       inverse.
   \end{proof}
 
@@ -8769,10 +8812,9 @@
   \begin{theorem}[6A]
     For any sets $A$, $B$, and $C$,
       \begin{enumerate}[(a)]
-        \item $\equinumerous{A}{A}$.
-        \item If $\equinumerous{A}{B}$, then $\equinumerous{B}{A}$.
-        \item If $\equinumerous{A}{B}$ and $\equinumerous{B}{C}$, then
-          $\equinumerous{A}{C}$.
+        \item $A \equin A$.
+        \item If $A \equin B$, then $B \equin A$.
+        \item If $A \equin B$ and $B \equin C$, then $A \equin C$.
       \end{enumerate}
   \end{theorem}
 
@@ -8798,18 +8840,18 @@
 
     \paragraph{(b)}%
 
-      Suppose $\equinumerous{A}{B}$.
+      Suppose $A \equin B$.
       Then there exists a one-to-one correspondence $F$ between $A$ and $B$.
       Consider now \nameref{ref:inverse} $$F^{-1} = \{\tuple{u, v} \mid vFu\}.$$
       By \nameref{sub:one-to-one-inverse}, $F^{-1}$ is a one-to-one function.
       For all $y \in A$, $\tuple{y, F(y)} \in F$.
       Then $\tuple{F(y), y} \in F^{-1}$ meaning $F^{-1}$ is onto $A$.
       Hence $F^{-1}$ is a one-to-one correspondence between $B$ and $A$, i.e.
-        $\equinumerous{B}{A}$.
+        $B \equin A$.
 
     \paragraph{(c)}%
 
-      Suppose $\equinumerous{A}{B}$ and $\equinumerous{B}{C}$.
+      Suppose $A \equin B$ and $B \equin C$.
       Then there exists a one-to-one correspondence $G$ between $A$ and $B$ and
         a one-to-one correspondence $F$ between $B$ and $C$.
       By \nameref{sub:one-to-one-composition}, $F \circ G$ is a one-to-one
@@ -8823,7 +8865,7 @@
       Then $F(G(x)) = y$.
       Thus $\ran{(F \circ G)} = C$ meaning $F \circ G$ is onto $C$.
       Hence $F \circ G$ is a one-to-one correspondence function between $A$ and
-        $C$, i.e. $\equinumerous{A}{C}$.
+        $C$, i.e. $A \equin C$.
 
   \end{proof}
 
@@ -8957,13 +8999,13 @@
 
   \begin{proof}
     Let $S$ be a \nameref{ref:finite-set} and $S'$ be a
-      \nameref{ref:proper-subset} $S'$ of $S$.
+      \nameref{ref:proper-subset} of $S$.
     Then there exists some set $T$, disjoint from $S'$, such that
       $S' \cup T = S$.
     By definition of a \nameref{ref:finite-set}, $S$ is
       \nameref{ref:equinumerous} to a natural number $n$.
-    By \nameref{sub:theorem-6a}, $\equinumerous{S' \cup T}{S}$ which, by the
-      same theorem, implies $\equinumerous{S' \cup T}{n}$.
+    By \nameref{sub:theorem-6a}, $S' \cup T \equin S$ which, by the same
+      theorem, implies $S' \cup T \equin n$.
 
     Let $f$ be a one-to-one correspondence between $S' \cup T$ and $n$.
     Then $f \restriction S'$ is a one-to-one correspondence between $S'$ and a
@@ -9060,8 +9102,8 @@
     By \nameref{sub:trichotomy-law-natural-numbers}, exactly one of three
       situations is possible: $n = m$, $n < m$, or $m < n$.
 
-    If $n < m$, then $\equinumerous{m}{S}$ and $\equinumerous{S}{n}$.
-    By \nameref{sub:theorem-6a}, it follows $\equinumerous{m}{n}$.
+    If $n < m$, then $m \equin S$ and $S \equin n$.
+    By \nameref{sub:theorem-6a}, it follows $m \equin n$.
     But \nameref{sub:pigeonhole-principle} indicates no natural number is
       equinumerous to a proper subset of itself, a contradiction.
     If $m < n$, a parallel argument applies.
@@ -9073,7 +9115,7 @@
 \hyperlabel{sub:lemma-6f}
 
   \begin{lemma}[6F]
-    If $C$ is a proper subset of a natural number $n$, then $C \approx m$ for
+    If $C$ is a proper subset of a natural number $n$, then $C \equin m$ for
       some $m$ less than $n$.
   \end{lemma}
 
@@ -9086,7 +9128,7 @@
       \begin{equation}
         \hyperlabel{sub:lemma-6f-eq1}
         S = \{n \in \omega \mid \forall C \subset n,
-          \exists m < n \text{ such that } \equinumerous{C}{m}\}.
+          \exists m < n \text{ such that } C \equin m\}.
       \end{equation}
     We prove that (i) $0 \in S$ and (ii) if $n \in S$ then $n^+ \in S$.
     Afterward we prove (iii) the lemma statement.
@@ -9143,7 +9185,7 @@
         \nameref{ref:inductive-set}.
       By \nameref{sub:theorem-4b}, $S = \omega$.
       Therefore, for every proper subset $C$ of a natural number $n$, there
-        exists some $m < n$ such that $\equinumerous{C}{n}$.
+        exists some $m < n$ such that $C \equin n$.
 
   \end{proof}
 
@@ -9162,26 +9204,232 @@
     Clearly, if $S' = S$, then $S'$ is finite.
     Therefore suppose $S'$ is a proper subset of $S$.
 
-    By definition of finite set, $S$ is \nameref{ref:equinumerous} to some
+    By definition of a finite set, $S$ is \nameref{ref:equinumerous} to some
       natural number $n$.
     Let $f$ be a one-to-one correspondence between $S$ and $n$.
     Then $f \restriction S'$ is a one-to-one correspondence between $S'$ and
       some proper subset of $n$.
     By \nameref{sub:lemma-6f}, $\ran{(f \restriction S')}$ is equinumerous to
       some $m < n$.
-    Then \nameref{sub:theorem-6a} indicates $\equinumerous{S'}{m}$.
+    Then \nameref{sub:theorem-6a} indicates $S' \equin m$.
     Hence $S'$ is a finite set.
   \end{proof}
 
+\subsection{\verified{Subset Size}}%
+\hyperlabel{sub:subset-size}
+
+  \begin{lemma}
+    Let $A$ be a finite set and $B \subseteq A$.
+    Then there exist natural numbers $m, n \in \omega$ such that
+      $B \equin m$, $A \equin n$, and $m \leq n$.
+  \end{lemma}
+
+  \code{Bookshelf/Enderton/Set/Chapter\_6}
+    {Enderton.Set.Chapter\_6.subset\_size}
+
+  \begin{proof}
+
+    Let $A$ be a \nameref{ref:finite-set} and $B$ be a subset of $A$.
+    By \nameref{sub:corollary-6g}, $B$ must be finite.
+    By definition of a finite set, there exists natural numbers
+      $m, n \in \omega$ such that $B \equin m$ and $A \equin n$.
+    By \nameref{sub:trichotomy-law-natural-numbers}, it suffices to prove that
+      $m > n$ is not possible for then either $m < n$ or $m = n$.
+
+    For the sake of contradiction, assume $m > n$.
+    By definition of \nameref{ref:equinumerous}, there exists a one-to-one
+      correspondence between $B$ and $m$.
+    \nameref{sub:theorem-6a} indicates there then exists a one-to-one
+      correspondence $f$ between $m$ and $B$.
+    Likewise, there exists a one-to-one correspondence $g$ between $A$ and
+      $n$.
+
+    Define $h \colon A \rightarrow B$ as $h(x) = f(g(x))$ for all $x \in A$.
+    Since $n \subset m$ by \nameref{sub:corollary-4m}, $h$ is well-defined.
+    By \nameref{sub:one-to-one-composition}, $h$ must be one-to-one.
+    Thus $h$ is a one-to-one correspondence between $A$ and $\ran{h}$, i.e.
+      $A \equin \ran{h}$.
+    But $n < m$ meaning $\ran{h} \subset B$ which in turn is a proper subset
+      of $A$ by hypothesis.
+    \nameref{sub:corollary-6c} states no finite set is equinumerous to a
+      proper subset of itself, a contradiction.
+
+  \end{proof}
+
+\subsection{\pending{Finite Domain and Range Size}}%
+\hyperlabel{sub:finite-domain-range-size}
+
+  \begin{lemma}
+    Let $A$ and $B$ be finite sets and $f \colon A \rightarrow B$ be a function.
+    Then there exist natural numbers $m, n \in \omega$ such that
+      $\dom{f} \equin m$, $\ran{f} \equin n$, and $m \geq n$.
+  \end{lemma}
+
+  \begin{note}
+    This proof avoids the \nameref{ref:axiom-of-choice-1} because $A$ and $B$
+      are finite.
+    In particular, we are able to choose a "smallest" element of each preimage
+      set.
+    Contrast this to \nameref{sub:theorem-3j-b}.
+  \end{note}
+
+  \begin{proof}
+    Let $A$ and $B$ be \nameref{ref:finite-set}s and $f \colon A \rightarrow B$
+      be a function.
+    By definition of finite sets, there exists \nameref{ref:natural-number}s
+      $m, p \in \omega$ such that $A \equin m$ and $B \equin p$.
+    By definition of the \nameref{ref:domain} of a function, $\dom{f} = A$.
+    Thus $\dom{f} \equin m$.
+
+    By \nameref{sub:theorem-6a}, there exists a one-to-one correspondence $g$
+      between $m$ and $\dom{f} = A$.
+    For all $y \in \ran{f}$, consider $\img{f^{-1}}{\{y\}}$.
+    Let $$A_y = \{ x \in m \mid f(g(x)) = y \}.$$
+    Since $g$ is a one-to-one correspondence, it follows that
+      $A_y \equin \img{f^{-1}}{\{y\}}$.
+    Since $A_y$ is a nonempty subset of natural numbers, the
+      \nameref{sub:well-ordering-natural-numbers} implies there exists a least
+      element, say $q_y$.
+    Define $C = \{q_y \mid y \in \ran{f}\}$.
+    Thus $h \colon C \rightarrow \ran{f}$ given by $h(x) = f(g(x))$ is a
+      one-to-one correspondence between $C$ and $\ran{f}$ by construction.
+    That is, $C \equin \ran{f}$.
+    By \nameref{sub:lemma-6f}, there exists some $n \leq m$ such that
+      $C \equin n$.
+    By \nameref{sub:theorem-6a}, $n \equin \ran{f}$.
+  \end{proof}
+
+\subsection{\verified{Set Difference Size}}%
+\hyperlabel{sub:set-difference-size}
+
+  \begin{lemma}
+    Let $A \equin m$ for some natural number $m$ and $B \subseteq A$.
+    Then there exists some $n \in \omega$ such that $n \leq m$, $B \equin n$,
+      and $A - B \equin m - n$.
+  \end{lemma}
+
+  \code{Bookshelf/Enderton/Set/Chapter\_6}
+    {Enderton.Set.Chapter\_6.sdiff\_size}
+
+  \begin{proof}
+
+    Let
+      \begin{equation}
+        \hyperlabel{sub:set-difference-size-ih}
+        S = \{m \in \omega \mid
+          \forall A \equin m, \forall B \subseteq A, \exists n
+            \in \omega (n \leq m \land B \equin n \land A - B \equin m - n)\}.
+      \end{equation}
+    We prove that (i) $0 \in S$ and (ii) if $n \in S$ then $n^+ \in S$.
+    Afterward we prove (iii) the lemma statement.
+
+    \paragraph{(i)}%
+    \hyperlabel{par:set-difference-size-i}
+
+      Let $A \equin 0$ and $B \subseteq A$.
+      Then it follows $A = B = \emptyset = 0$.
+      Since $0 \leq 0$, $B \equin 0$, and $A - B = \emptyset \equin 0 = 0 - 0$,
+        it follows $0 \in S$.
+
+    \paragraph{(ii)}%
+    \hyperlabel{par:set-difference-size-ii}
+
+      Suppose $m \in S$ and consider $m^+$.
+      Let $A \equin m^+$ and let $B \subseteq A$.
+      By definition of \nameref{ref:equinumerous}, there exists a one-to-one
+        correspondence $f$ between $A$ and $m^+$.
+      Since $f$ is one-to-one and onto, there exists a unique value $a \in A$
+        such that $f(a) = m$.
+      Then $B - \{a\} \subseteq A - \{a\}$ and $f$ is a one-to-one
+        correspondence between $A - \{a\}$ and $m$.
+      By \ihref{sub:set-difference-size-ih}, there exists some $n \in \omega$
+        such that $n \leq m$, $B - \{a\} \equin n$ and
+        \begin{equation}
+          \hyperlabel{par:set-difference-size-ii-eq1}
+          (A - \{a\}) - (B - \{a\}) \equin m - n.
+        \end{equation}
+      There are two cases to consider:
+
+      \subparagraph{Case 1}%
+
+        Assume $a \in B$.
+        Then $B \equin n^+$.
+        Furthermore, by definition of the set difference,
+          \begin{align}
+            (A - \{a\}) & - (B - \{a\}) \nonumber \\
+              & = \{x \mid
+                x \in A - \{a\} \land x \not\in B - \{a\}\} \nonumber \\
+              & = \{x \mid
+                (x \in A \land x \neq a) \land
+                \neg(x \in B \land x \neq a)\} \nonumber \\
+              & = \{x \mid
+                (x \in A \land x \neq a) \land
+                (x \not\in B \lor x = a)\} \nonumber \\
+              & = \{x \mid
+                (x \in A \land x \neq a \land x \not\in B) \lor
+                (x \in A \land x \neq a \land x = a)\} \nonumber \\
+              & = \{x \mid
+                (x \in A \land x \neq a \land x \not\in B) \lor F\} \nonumber \\
+              & = \{x \mid
+                (x \in A \land x \neq a \land x \not\in B)\} \nonumber \\
+              & = \{x \mid x \in A - B \land x \neq a\} \nonumber \\
+              & = \{x \mid x \in A - B \land x \not\in \{a\}\} \nonumber \\
+              & = (A - B) - \{a\}.
+                \hyperlabel{par:set-difference-size-ii-eq2}
+          \end{align}
+        Since $a \in A$ and $a \in B$, $(A - B) - \{a\} = A - B$.
+        Thus
+          \begin{align*}
+            (A - \{a\} - (B - \{a\})
+              & = (A - B) - \{a\} & \eqref{par:set-difference-size-ii-eq2} \\
+              & = A - B \\
+              & \equin m - n & \eqref{par:set-difference-size-ii-eq1} \\
+              & \equin m^+ - n^+.
+          \end{align*}
+
+      \subparagraph{Case 2}%
+
+        Assume $a \not\in B$.
+        Then $B - \{a\} = B$ (i.e. $B \approx n$) and
+          \begin{align*}
+            (A - \{a\}) - (B - \{a\})
+              & = (A - \{a\}) - B \\
+              & \equin m - n. & \eqref{par:set-difference-size-ii-eq1}
+          \end{align*}
+        The above implies that there exists a one-to-one correspondence $g$
+          between $(A - \{a\}) - B$ and $m - n$.
+        Therefore $g \cup \{\tuple{a, m}\}$ is a one-to-one correspondence
+          between $A - B$ and $(m - n) \cup \{m\}$.
+        Hence $$A - B \equin (m - n) \cup \{m\} \equin m^+ - n.$$
+
+      \subparagraph{Subconclusion}%
+
+        The above two cases are exhaustive and both conclude the existence of
+          some $n \in \omega$ such that $n \leq m^+$, $B \equin n$ and
+          $A - B \equin m^+ - n$.
+        Hence $m^+ \in S$.
+
+    \paragraph{(iii)}%
+
+      By \nameref{par:set-difference-size-i} and
+        \nameref{par:set-difference-size-ii}, $S \subseteq \omega$ is an
+        \nameref{ref:inductive-set}.
+      Thus \nameref{sub:theorem-4b} implies $S = \omega$.
+      Hence, for all $A \equin m$ for some $m \in \omega$, if $B \subseteq A$,
+        then there exists some $n \in \omega$ such that $n \leq m$,
+        $B \equin n$, and $A - B \equin m - n$.
+
+  \end{proof}
+
 \subsection{\sorry{Theorem 6H}}%
 \hyperlabel{sub:theorem-6h}
 
-  Assume that $\equinumerous{K_1}{K_2}$ and $\equinumerous{L_1}{L_2}$.
+  Assume that $K_1 \equin K_2$ and $L_1 \equin L_2$.
     \begin{enumerate}[(a)]
       \item If $K_1 \cap L_1 = K_2 \cap L_2 = \emptyset$, then
-        $\equinumerous{K_1 \cup L_1}{K_2 \cup L_2}$.
-      \item $\equinumerous{K_1 \times L_1}{K_2 \times L_2}$.
-      \item $\equinumerous{^{(L_1)}{K_1}}{^{(L_2)}{K_2}}$.
+        $K_1 \cup L_1 \equin K_2 \cup L_2$.
+      \item $K_1 \times L_1 \equin K_2 \times L_2$.
+      \item $^{(L_1)}{K_1} \equin ^{(L_2)}{K_2}$.
     \end{enumerate}
 
   \begin{proof}
@@ -9530,7 +9778,7 @@
     Refer to \nameref{sub:theorem-6a}.
   \end{proof}
 
-\subsection{\sorry{Exercise 6.6}}%
+\subsection{\unverified{Exercise 6.6}}%
 \hyperlabel{sub:exercise-6.6}
 
   Let $\kappa$ be a nonzero cardinal number.
@@ -9538,20 +9786,74 @@
     belongs.
 
   \begin{proof}
-    TODO
+    Let $\kappa$ be a nonzero cardinal number and define
+      $$\mathbf{K}_\kappa = \{ X \mid \card{X} = \kappa \}.$$
+    For the sake of contradiction, suppose $\mathbf{K}_\kappa$ is a set.
+    Then the \nameref{ref:union-axiom} suggests $\bigcup \mathbf{K}_{\kappa}$ is
+      a set.
+    But this "set" is precisely the class of all sets, which is \textit{not} a
+      set.
+    Thus our original assumption was incorrect.
+    That is, there does not exist a set to which every set of cardinality
+      $\kappa$ belongs.
   \end{proof}
 
-\subsection{\sorry{Exercise 6.7}}%
+\subsection{\pending{Exercise 6.7}}%
 \hyperlabel{sub:exercise-6.7}
 
   Assume that $A$ is finite and $f \colon A \rightarrow A$.
   Show that $f$ is one-to-one iff $\ran{f} = A$.
 
+  \code*{Bookshelf/Enderton/Set/Chapter\_6}
+    {Enderton.Set.Chapter\_6.exercise\_6\_7}
+
   \begin{proof}
-    TODO
+    Let $A$ be a \nameref{ref:finite-set} and $f \colon A \rightarrow A$.
+
+    \paragraph{($\Rightarrow$)}%
+
+      Suppose $f$ is one-to-one.
+      Then $f$ is a one-to-one correspondence between $A$ and $\ran{f}$.
+      That is, $A \equin \ran{f}$.
+      Because $f$ maps $A$ onto $A$, $\ran{f} \subseteq A$.
+      Hence $\ran{f} \subset A$ or $\ran{f} = A$.
+      But, by \nameref{sub:corollary-6c}, $\ran{f}$ cannot be a proper subset of
+        $A$.
+      Thus $\ran{f} = A$.
+
+    \paragraph{($\Leftarrow$)}%
+
+      If $A = \emptyset$, then $f$ is trivially one-to-one.
+      Assume now $A \neq \emptyset$ and $\ran{f} = A$.
+      Let $x_1, x_2 \in A$ such that $f(x_1) = f(x_2) = y$ for some $y \in A$.
+      We must prove that $x_1 = x_2$.
+
+      Let $B = \img{f^{-1}}{\{y\}}$.
+      Then $x_1, x_2 \in B$.
+      Since $B \subseteq A$, \nameref{sub:subset-size} indicates that there
+        exist natural numbers $m_1, n_1 \in \omega$ such that $B \equin m_1$,
+        $A \equin n_1$, and $m_1 \leq n_1$.
+      Define $f' \colon (A - B) \rightarrow (A - \{y\})$ as the
+        \nameref{ref:restriction} of $f$ to $A - B$.
+      Since $\ran{f} = A$, it follows $\ran{f'} = A - \{y\}$.
+      Since \nameref{sub:corollary-6g} implies $A - B$ and $A - \{y\}$ are
+        finite sets, \nameref{sub:finite-domain-range-size} implies the
+        existence of natural numbers $m_2, n_2 \in \omega$ such that
+        $\dom{f'} \equin m_2$, $\ran{f'} \equin n_2$, and $m_2 \geq n_2$.
+      Thus, by \nameref{sub:set-difference-size},
+        \begin{align*}
+          m_2 & \equin \dom{f'} \equin A - B \equin n_1 - m_1 \\
+          n_2 & \equin \ran{f'} \equin A - \{y\} \equin n_1 - 1.
+        \end{align*}
+      By \nameref{sub:corollary-6e}, $m_2 = n_1 - m_1$ and $n_2 = n_1 - 1$.
+      Since $m_2 \geq n_2$, $n_1 - m_1 \geq n_1 - 1$.
+      But $1 \leq m_1 \leq n_1$ meaning $m_1 = 1$.
+      Hence $B$ is a singleton.
+      Therefore $x_1 = x_2$, i.e. $f$ is one-to-one.
+
   \end{proof}
 
-\subsection{\sorry{Exercise 6.8}}%
+\subsection{\pending{Exercise 6.8}}%
 \hyperlabel{sub:exercise-6.8}
 
   Prove that the union of two finite sets is finite, without any use of
@@ -9561,7 +9863,7 @@
     TODO
   \end{proof}
 
-\subsection{\sorry{Exercise 6.9}}%
+\subsection{\pending{Exercise 6.9}}%
 \hyperlabel{sub:exercise-6.9}
 
   Prove that the Cartesian product of two finite sets is finite, without any use

Bookshelf/Enderton/Set/Chapter_1.lean

@@ -19,7 +19,7 @@ The `∅` does not equal the singleton set containing `∅`.
 lemma empty_ne_singleton_empty (h : ∅ = ({∅} : Set (Set α))) : False :=
   absurd h (Ne.symm $ Set.singleton_ne_empty (∅ : Set α))
 
-/-- #### Exercise 1.1a
+/-- ### Exercise 1.1a
 
 `{∅} ___ {∅, {∅}}`
 -/
@@ -27,7 +27,7 @@ theorem exercise_1_1a
   : {∅} ∈ ({∅, {∅}} : Set (Set (Set α)))
   ∧ {∅} ⊆ ({∅, {∅}} : Set (Set (Set α))) := ⟨by simp, by simp⟩
 
-/-- #### Exercise 1.1b
+/-- ### Exercise 1.1b
 
 `{∅} ___ {∅, {{∅}}}`
 -/
@@ -39,7 +39,7 @@ theorem exercise_1_1b
   simp at h
   exact empty_ne_singleton_empty h
 
-/-- #### Exercise 1.1c
+/-- ### Exercise 1.1c
 
 `{{∅}} ___ {∅, {∅}}`
 -/
@@ -47,7 +47,7 @@ theorem exercise_1_1c
   : {{∅}} ∉ ({∅, {∅}} : Set (Set (Set (Set α))))
   ∧ {{∅}} ⊆ ({∅, {∅}} : Set (Set (Set (Set α)))) := ⟨by simp, by simp⟩
 
-/-- #### Exercise 1.1d
+/-- ### Exercise 1.1d
 
 `{{∅}} ___ {∅, {{∅}}}`
 -/
@@ -59,7 +59,7 @@ theorem exercise_1_1d
   simp at h
   exact empty_ne_singleton_empty h
 
-/-- #### Exercise 1.1e
+/-- ### Exercise 1.1e
 
 `{{∅}} ___ {∅, {∅, {∅}}}`
 -/
@@ -126,4 +126,4 @@ theorem exercise_1_4 (x y : α) (hx : x ∈ B) (hy : y ∈ B)
       (Set.singleton_subset_iff.mpr hx)
       (Set.singleton_subset_iff.mpr hy)
 
-end Enderton.Set.Chapter_1
+end Enderton.Set.Chapter_1

Bookshelf/Enderton/Set/Chapter_2.lean

@@ -10,7 +10,7 @@ Axioms and Operations
 
 namespace Enderton.Set.Chapter_2
 
-/-! #### Commutative Laws
+/-! ### Commutative Laws
 
 For any sets `A` and `B`,
 ```
@@ -20,7 +20,8 @@ A ∩ B = B ∩ A
 -/
 
 theorem commutative_law_i (A B : Set α)
-  : A ∪ B = B ∪ A := calc A ∪ B
+  : A ∪ B = B ∪ A :=
+  calc A ∪ B
   _ = { x | x ∈ A ∨ x ∈ B } := rfl
   _ = { x | x ∈ B ∨ x ∈ A } := by
     ext
@@ -39,7 +40,7 @@ theorem commutative_law_ii (A B : Set α)
 
 #check Set.inter_comm
 
-/-! #### Associative Laws
+/-! ### Associative Laws
 
 For any sets `A`, `B`, and `C`,
 ```
@@ -74,7 +75,7 @@ theorem associative_law_ii (A B C : Set α)
 
 #check Set.inter_assoc
 
-/-! #### Distributive Laws
+/-! ### Distributive Laws
 
 For any sets `A`, `B`, and `C`,
 ```
@@ -107,7 +108,7 @@ theorem distributive_law_ii (A B C : Set α)
 
 #check Set.union_distrib_left
 
-/-! #### De Morgan's Laws
+/-! ### De Morgan's Laws
 
 For any sets `A`, `B`, and `C`,
 ```
@@ -148,7 +149,7 @@ theorem de_morgans_law_ii (A B C : Set α)
 
 #check Set.diff_inter
 
-/-! #### Identities Involving ∅
+/-! ### Identities Involving ∅
 
 For any set `A`,
 ```
@@ -171,8 +172,7 @@ theorem emptyset_identity_ii (A : Set α)
   : A ∩ ∅ = ∅ := calc A ∩ ∅
   _ = { x | x ∈ A ∧ x ∈ ∅ } := rfl
   _ = { x | x ∈ A ∧ False } := rfl
-  _ = { x | False } := by simp
-  _ = ∅ := rfl
+  _ = ∅ := by simp
 
 #check Set.inter_empty
 
@@ -181,12 +181,11 @@ theorem emptyset_identity_iii (A C : Set α)
   _ = { x | x ∈ A ∧ x ∈ C \ A } := rfl
   _ = { x | x ∈ A ∧ (x ∈ C ∧ x ∉ A) } := rfl
   _ = { x | x ∈ C ∧ False } := by simp
-  _ = { x | False } := by simp
-  _ = ∅ := rfl
+  _ = ∅ := by simp
 
 #check Set.inter_diff_self
 
-/-! #### Monotonicity
+/-! ### Monotonicity
 
 For any sets `A`, `B`, and `C`,
 ```
@@ -230,7 +229,7 @@ theorem monotonicity_iii (A B : Set (Set α)) (h : A ⊆ B)
 
 #check Set.sUnion_mono
 
-/-! #### Anti-monotonicity
+/-! ### Anti-monotonicity
 
 For any sets `A`, `B`, and `C`,
 ```
@@ -262,7 +261,7 @@ theorem anti_monotonicity_ii (A B : Set (Set α)) (h : A ⊆ B)
 
 #check Set.sInter_subset_sInter
 
-/-- #### Intersection/Difference Associativity
+/-- ### Intersection/Difference Associativity
 
 Let `A`, `B`, and `C` be sets. Then `A ∩ (B - C) = (A ∩ B) - C`.
 -/
@@ -279,7 +278,7 @@ theorem inter_diff_assoc (A B C : Set α)
 
 #check Set.inter_diff_assoc
 
-/-- #### Exercise 2.1
+/-- ### Exercise 2.1
 
 Assume that `A` is the set of integers divisible by `4`. Similarly assume that
 `B` and `C` are the sets of integers divisible by `9` and `10`, respectively.
@@ -301,7 +300,7 @@ theorem exercise_2_1 {A B C : Set ℤ}
   · rw [hC] at hc
     exact Set.mem_setOf.mp hc
 
-/-- #### Exercise 2.2
+/-- ### Exercise 2.2
 
 Give an example of sets `A` and `B` for which `⋃ A = ⋃ B` but `A ≠ B`.
 -/
@@ -340,7 +339,7 @@ theorem exercise_2_2 {A B : Set (Set ℕ)}
     have h₂ := h₁ 2
     simp at h₂
 
-/-- #### Exercise 2.3
+/-- ### Exercise 2.3
 
 Show that every member of a set `A` is a subset of `U A`. (This was stated as an
 example in this section.)
@@ -353,7 +352,7 @@ theorem exercise_2_3 {A : Set (Set α)}
   rw [Set.mem_setOf_eq]
   exact ⟨x, ⟨hx, hy⟩⟩
 
-/-- #### Exercise 2.4
+/-- ### Exercise 2.4
 
 Show that if `A ⊆ B`, then `⋃ A ⊆ ⋃ B`.
 -/
@@ -365,7 +364,7 @@ theorem exercise_2_4 {A B : Set (Set α)} (h : A ⊆ B) : ⋃₀ A ⊆ ⋃₀ B
   rw [Set.mem_setOf_eq]
   exact ⟨t, ⟨h ht, hxt⟩⟩
 
-/-- #### Exercise 2.5
+/-- ### Exercise 2.5
 
 Assume that every member of `𝓐` is a subset of `B`. Show that `⋃ 𝓐 ⊆ B`.
 -/
@@ -377,7 +376,7 @@ theorem exercise_2_5 {𝓐 : Set (Set α)} (h : ∀ x ∈ 𝓐, x ⊆ B)
   have ⟨t, ⟨ht𝓐, hyt⟩⟩ := hy
   exact (h t ht𝓐) hyt
 
-/-- #### Exercise 2.6a
+/-- ### Exercise 2.6a
 
 Show that for any set `A`, `⋃ 𝓟 A = A`.
 -/
@@ -394,7 +393,7 @@ theorem exercise_2_6a : ⋃₀ (𝒫 A) = A := by
     rw [Set.mem_setOf_eq]
     exact ⟨A, ⟨by rw [Set.mem_setOf_eq], hx⟩⟩
 
-/-- #### Exercise 2.6b
+/-- ### Exercise 2.6b
 
 Show that `A ⊆ 𝓟 ⋃ A`. Under what conditions does equality hold?
 -/
@@ -413,7 +412,7 @@ theorem exercise_2_6b
       conv => rhs; rw [hB, exercise_2_6a]
       exact hB
 
-/-- #### Exercise 2.7a
+/-- ### Exercise 2.7a
 
 Show that for any sets `A` and `B`, `𝓟 A ∩ 𝓟 B = 𝓟 (A ∩ B)`.
 -/
@@ -431,7 +430,7 @@ theorem exercise_2_7A
     intro x hA _
     exact hA
 
-/-- #### Exercise 2.7b (i)
+/-- ### Exercise 2.7b (i)
 
 Show that `𝓟 A ∪ 𝓟 B ⊆ 𝓟 (A ∪ B)`.
 -/
@@ -448,7 +447,7 @@ theorem exercise_2_7b_i
     rw [Set.mem_setOf_eq]
     exact Set.subset_union_of_subset_right hB A
 
-/-- #### Exercise 2.7b (ii)
+/-- ### Exercise 2.7b (ii)
 
 Under what conditions does `𝓟 A ∪ 𝓟 B = 𝓟 (A ∪ B)`.?
 -/
@@ -500,7 +499,7 @@ theorem exercise_2_7b_ii
         refine Or.inl (Set.Subset.trans hx ?_)
         exact subset_of_eq (Set.right_subset_union_eq_self hB)
 
-/-- #### Exercise 2.9
+/-- ### Exercise 2.9
 
 Give an example of sets `a` and `B` for which `a ∈ B` but `𝓟 a ∉ 𝓟 B`.
 -/
@@ -528,7 +527,7 @@ theorem exercise_2_9 (ha : a = {1}) (hB : B = {{1}})
       have := h 1
       simp at this
 
-/-- #### Exercise 2.10
+/-- ### Exercise 2.10
 
 Show that if `a ∈ B`, then `𝓟 a ∈ 𝓟 𝓟 ⋃ B`.
 -/
@@ -541,7 +540,7 @@ theorem exercise_2_10 {B : Set (Set α)} (ha : a ∈ B)
   rw [← hb, Set.mem_setOf_eq]
   exact h₂
 
-/-- #### Exercise 2.11 (i)
+/-- ### Exercise 2.11 (i)
 
 Show that for any sets `A` and `B`, `A = (A ∩ B) ∪ (A - B)`.
 -/
@@ -558,7 +557,7 @@ theorem exercise_2_11_i {A B : Set α}
   · intro hx
     exact ⟨hx, em (B x)⟩
 
-/-- #### Exercise 2.11 (ii)
+/-- ### Exercise 2.11 (ii)
 
 Show that for any sets `A` and `B`, `A ∪ (B - A) = A ∪ B`.
 -/
@@ -617,7 +616,7 @@ lemma right_diff_eq_insert_one_three : A \ (B \ C) = {1, 3} := by
       rw [hy] at hz
       unfold Membership.mem Set.instMembershipSet Set.Mem at hz
       unfold singleton Set.instSingletonSet Set.singleton setOf at hz
-      simp only at hz
+      simp at hz
     · intro hy
       refine ⟨Or.inr (Or.inr hy), ?_⟩
       intro hz
@@ -636,7 +635,7 @@ lemma left_diff_eq_singleton_one : (A \ B) \ C = {1} := by
     have ⟨⟨ha, hb⟩, hc⟩ := hx
     rw [not_or_de_morgan] at hb hc
     apply Or.elim ha
-    · simp 
+    · simp
     · intro hy
       apply Or.elim hy
       · intro hz
@@ -652,7 +651,7 @@ lemma left_diff_eq_singleton_one : (A \ B) \ C = {1} := by
         | inl y => rw [hx] at y; simp at y
         | inr y => rw [hx] at y; simp at y
 
-/-- #### Exercise 2.14
+/-- ### Exercise 2.14
 
 Show by example that for some sets `A`, `B`, and `C`, the set `A - (B - C)` is
 different from `(A - B) - C`.
@@ -669,7 +668,7 @@ theorem exercise_2_14 : A \ (B \ C) ≠ (A \ B) \ C := by
 
 end
 
-/-- #### Exercise 2.15 (a)
+/-- ### Exercise 2.15 (a)
 
 Show that `A ∩ (B + C) = (A ∩ B) + (A ∩ C)`.
 -/
@@ -697,7 +696,7 @@ theorem exercise_2_15a (A B C : Set α)
 
 #check Set.inter_symmDiff_distrib_left
 
-/-- #### Exercise 2.15 (b)
+/-- ### Exercise 2.15 (b)
 
 Show that `A + (B + C) = (A + B) + C`.
 -/
@@ -750,7 +749,7 @@ theorem exercise_2_15b (A B C : Set α)
 
 #check symmDiff_assoc
 
-/-- #### Exercise 2.16
+/-- ### Exercise 2.16
 
 Simplify:
 `[(A ∪ B ∪ C) ∩ (A ∪ B)] - [(A ∪ (B - C)) ∩ A]`
@@ -762,7 +761,7 @@ theorem exercise_2_16 {A B C : Set α}
     _ = (A ∪ B) \ A := by rw [Set.union_inter_cancel_left]
     _ = B \ A := by rw [Set.union_diff_left]
 
-/-! #### Exercise 2.17
+/-! ### Exercise 2.17
 
 Show that the following four conditions are equivalent.
 
@@ -792,13 +791,13 @@ theorem exercise_2_17_ii {A B : Set α} (h : A \ B = ∅)
 
 theorem exercise_2_17_iii {A B : Set α} (h : A ∪ B = B)
   : A ∩ B = A := by
-  suffices A ⊆ B from Set.inter_eq_left_iff_subset.mpr this
-  exact Set.union_eq_right_iff_subset.mp h
+  suffices A ⊆ B from Set.inter_eq_left.mpr this
+  exact Set.union_eq_right.mp h
 
 theorem exercise_2_17_iv {A B : Set α} (h : A ∩ B = A)
-  : A ⊆ B := Set.inter_eq_left_iff_subset.mp h
+  : A ⊆ B := Set.inter_eq_left.mp h
 
-/-- #### Exercise 2.19
+/-- ### Exercise 2.19
 
 Is `𝒫 (A - B)` always equal to `𝒫 A - 𝒫 B`? Is it ever equal to `𝒫 A - 𝒫 B`?
 -/
@@ -811,7 +810,7 @@ theorem exercise_2_19 {A B : Set α}
   have := h ∅
   exact absurd (this.mp he) ne
 
-/-- #### Exercise 2.20
+/-- ### Exercise 2.20
 
 Let `A`, `B`, and `C` be sets such that `A ∪ B = A ∪ C` and `A ∩ B = A ∩ C`.
 Show that `B = C`.
@@ -837,7 +836,7 @@ theorem exercise_2_20 {A B C : Set α}
       rw [← hu] at this
       exact Or.elim this (absurd · hA) (by simp)
 
-/-- #### Exercise 2.21
+/-- ### Exercise 2.21
 
 Show that `⋃ (A ∪ B) = (⋃ A) ∪ (⋃ B)`.
 -/
@@ -861,7 +860,7 @@ theorem exercise_2_21 {A B : Set (Set α)}
       have ⟨t, ht⟩ : ∃ t, t ∈ B ∧ x ∈ t := hB
       exact ⟨t, ⟨Set.mem_union_right A ht.left, ht.right⟩⟩
 
-/-- #### Exercise 2.22
+/-- ### Exercise 2.22
 
 Show that if `A` and `B` are nonempty sets, then `⋂ (A ∪ B) = ⋂ A ∩ ⋂ B`.
 -/
@@ -890,7 +889,7 @@ theorem exercise_2_22 {A B : Set (Set α)}
     · intro hB
       exact (this t).right hB
 
-/-- #### Exercise 2.24a
+/-- ### Exercise 2.24a
 
 Show that is `𝓐` is nonempty, then `𝒫 (⋂ 𝓐) = ⋂ { 𝒫 X | X ∈ 𝓐 }`.
 -/
@@ -909,7 +908,7 @@ theorem exercise_2_24a {𝓐 : Set (Set α)}
     _ = { x | ∀ t ∈ { 𝒫 X | X ∈ 𝓐 }, x ∈ t} := by simp
     _ = ⋂₀ { 𝒫 X | X ∈ 𝓐 } := rfl
 
-/-- #### Exercise 2.24b
+/-- ### Exercise 2.24b
 
 Show that
 ```
@@ -951,10 +950,10 @@ theorem exercise_2_24b {𝓐 : Set (Set α)}
     simp only [Set.mem_setOf_eq, exists_exists_and_eq_and, Set.mem_powerset_iff]
     exact ⟨⋃₀ 𝓐, ⟨hA, hx⟩⟩
 
-/-- #### Exercise 2.25
+/-- ### Exercise 2.25
 
 Is `A ∪ (⋃ 𝓑)` always the same as `⋃ { A ∪ X | X ∈ 𝓑 }`? If not, then under
-what conditions does equality hold? 
+what conditions does equality hold?
 -/
 theorem exercise_2_25 {A : Set α} (𝓑 : Set (Set α))
   : (A ∪ (⋃₀ 𝓑) = ⋃₀ { A ∪ X | X ∈ 𝓑 }) ↔ (A = ∅ ∨ Set.Nonempty 𝓑) := by
@@ -995,4 +994,4 @@ theorem exercise_2_25 {A : Set α} (𝓑 : Set (Set α))
         _ = { x | ∃ t, t ∈ { y | ∃ X, X ∈ 𝓑 ∧ A ∪ X = y } ∧ x ∈ t } := by simp
         _ = ⋃₀ { A ∪ X | X ∈ 𝓑 } := rfl
 
-end Enderton.Set.Chapter_2
+end Enderton.Set.Chapter_2

Bookshelf/Enderton/Set/Chapter_3.lean

@@ -17,30 +17,51 @@ namespace Enderton.Set.Chapter_3
 
 open Set.Relation
 
-/-- #### Lemma 3B
+/-- ### Lemma 3B
 
 If `x ∈ C` and `y ∈ C`, then `⟨x, y⟩ ∈ 𝒫 𝒫 C`.
 -/
 lemma lemma_3b {C : Set α} (hx : x ∈ C) (hy : y ∈ C)
   : OrderedPair x y ∈ 𝒫 𝒫 C := by
+/-
+> Let `C` be an arbitrary set and `x, y ∈ C`. Then by definition of the power
+> set, `{x}` and `{x, y}` are members of `𝒫 C`.
+-/
   have hxs : {x} ⊆ C := Set.singleton_subset_iff.mpr hx
   have hxys : {x, y} ⊆ C := Set.mem_mem_imp_pair_subset hx hy
+/-
+> Likewise `{{x}, {x, y}}` is a member of `𝒫 𝒫 C`. By definition of an ordered
+> pair, `⟨x, y⟩ = {{x}, {x, y}}`. This concludes our proof.
+-/
   exact Set.mem_mem_imp_pair_subset hxs hxys
 
-/-- #### Theorem 3D
+/-- ### Theorem 3D
 
 If `⟨x, y⟩ ∈ A`, then `x` and `y` belong to `⋃ ⋃ A`.
 -/
 theorem theorem_3d {A : Set (Set (Set α))} (h : OrderedPair x y ∈ A)
   : x ∈ ⋃₀ (⋃₀ A) ∧ y ∈ ⋃₀ (⋃₀ A) := by
+/-
+> Let `A` be a set and `⟨x, y⟩ ∈ A`. By definition of an ordered pair,
+>
+> `⟨x, y⟩ = {{x}, {x, y}}`.
+>
+> By Exercise 2.3, `{{x}, {x, y}} ⊆ ∪ A`. Then `{x, y} ∈ ∪ A`.
+-/
   have hp := Chapter_2.exercise_2_3 (OrderedPair x y) h
-  unfold OrderedPair at hp  
+  unfold OrderedPair at hp
   have hq : {x, y} ∈ ⋃₀ A := hp (by simp)
+/-
+> Another application of Exercise 2.3 implies `{x, y} ∈ ∪ ∪ A`.
+-/
   have : {x, y} ⊆ ⋃₀ ⋃₀ A := Chapter_2.exercise_2_3 {x, y} hq
+/-
+> Therefore `x, y ∈ ∪ ∪ A`.
+-/
   exact ⟨this (by simp), this (by simp)⟩
 
 
-/-- #### Theorem 3G (i)
+/-- ### Theorem 3G (i)
 
 Assume that `F` is a one-to-one function. If `x ∈ dom F`, then `F⁻¹(F(x)) = x`.
 -/
@@ -54,7 +75,7 @@ theorem theorem_3g_i {F : Set.HRelation α β}
   unfold isOneToOne at hF
   exact (single_valued_eq_unique hF.left hy hy₁).symm
 
-/-- #### Theorem 3G (ii)
+/-- ### Theorem 3G (ii)
 
 Assume that `F` is a one-to-one function. If `y ∈ ran F`, then `F(F⁻¹(y)) = y`.
 -/
@@ -68,7 +89,7 @@ theorem theorem_3g_ii {F : Set.HRelation α β}
   unfold isOneToOne at hF
   exact (single_rooted_eq_unique hF.right hx hx₁).symm
 
-/-- #### Theorem 3H
+/-- ### Theorem 3H
 
 Assume that `F` and `G` are functions. Then
 ```
@@ -107,7 +128,7 @@ theorem theorem_3h_dom {F : Set.HRelation β γ} {G : Set.HRelation α β}
     simp only [Set.mem_setOf_eq]
     exact ⟨a, ha.left.left, hb⟩
 
-/-- #### Theorem 3J (a)
+/-- ### Theorem 3J (a)
 
 Assume that `F : A → B`, and that `A` is nonempty. There exists a function
 `G : B → A` (a "left inverse") such that `G ∘ F` is the identity function on `A`
@@ -199,7 +220,7 @@ theorem theorem_3j_a {F : Set.HRelation α β}
         Set.mem_union,
         Prod.mk.injEq
       ] at ht
-      have ⟨a₁, ha₁⟩ := ht 
+      have ⟨a₁, ha₁⟩ := ht
       apply Or.elim ha₁
       · intro ⟨⟨a, b, hab⟩, _⟩
         have := mem_pair_imp_fst_mem_dom hab.left
@@ -260,11 +281,11 @@ theorem theorem_3j_a {F : Set.HRelation α β}
     rw [← single_valued_eq_unique hF.is_func hx₂.right ht₂.left] at ht₂
     exact single_valued_eq_unique hG₁.is_func ht₂.right ht₁.right
 
-/-- #### Theorem 3J (b)
+/-- ### Theorem 3J (b)
 
 Assume that `F : A → B`, and that `A` is nonempty. There exists a function
 `H : B → A` (a "right inverse") such that `F ∘ H` is the identity function on
-`B` **iff** `F` maps `A` onto `B`.
+`B` only if `F` maps `A` onto `B`.
 -/
 theorem theorem_3j_b {F : Set.HRelation α β} (hF : mapsInto F A B)
   : (∃ H, mapsInto H B A ∧ comp F H = { p | p.1 ∈ B ∧ p.1 = p.2 }) →
@@ -279,7 +300,7 @@ theorem theorem_3j_b {F : Set.HRelation α β} (hF : mapsInto F A B)
   simp only [Set.mem_setOf_eq, Prod.exists, exists_eq_right, Set.setOf_mem_eq]
   exact hy
 
-/-- #### Theorem 3K (a)
+/-- ### Theorem 3K (a)
 
 The following hold for any sets. (`F` need not be a function.)
 The image of a union is the union of the images:
@@ -314,7 +335,7 @@ theorem theorem_3k_a {F : Set.HRelation α β} {𝓐 : Set (Set α)}
     simp only [Set.mem_sUnion, Set.mem_setOf_eq]
     exact ⟨u, ⟨A, hA.left, hu.left⟩, hu.right⟩
 
-/-! #### Theorem 3K (b)
+/-! ### Theorem 3K (b)
 
 The following hold for any sets. (`F` need not be a function.)
 The image of an intersection is included in the intersection of the images:
@@ -374,7 +395,7 @@ theorem theorem_3k_b_ii {F : Set.HRelation α β} {𝓐 : Set (Set α)}
   simp only [Set.mem_sInter, Set.mem_setOf_eq]
   exact ⟨u, hu⟩
 
-/-! #### Theorem 3K (c)
+/-! ### Theorem 3K (c)
 
 The following hold for any sets. (`F` need not be a function.)
 The image of a difference includes the difference of the images:
@@ -428,7 +449,7 @@ theorem theorem_3k_c_ii {F : Set.HRelation α β} {A B : Set α}
     exact absurd hu₁.left hu.left.right
   exact ⟨hv₁, hv₂⟩
 
-/-! #### Corollary 3L
+/-! ### Corollary 3L
 
 For any function `G` and sets `A`, `B`, and `𝓐`:
 
@@ -456,7 +477,7 @@ theorem corollary_3l_iii {G : Set.HRelation β α} {A B : Set α}
     single_valued_self_iff_single_rooted_inv.mp hG
   exact (theorem_3k_c_ii hG').symm
 
-/-- #### Theorem 3M
+/-- ### Theorem 3M
 
 If `R` is a symmetric and transitive relation, then `R` is an equivalence
 relation on `fld R`.
@@ -476,7 +497,7 @@ theorem theorem_3m {R : Set.Relation α}
     have := hS ht
     exact hT this ht
 
-/-- #### Theorem 3R
+/-- ### Theorem 3R
 
 Let `R` be a linear ordering on `A`.
 
@@ -500,7 +521,7 @@ theorem theorem_3r {R : Rel α α} (hR : IsStrictTotalOrder α R)
         right
         exact h₂
 
-/-- #### Exercise 3.1
+/-- ### Exercise 3.1
 
 Suppose that we attempted to generalize the Kuratowski definitions of ordered
 pairs to ordered triples by defining
@@ -521,9 +542,9 @@ theorem exercise_3_1 {x y z u v w : ℕ}
   · rw [hx, hy, hz, hu, hv, hw]
     simp
   · rw [hy, hv]
-    simp only
+    simp
 
-/-- #### Exercise 3.2a
+/-- ### Exercise 3.2a
 
 Show that `A × (B ∪ C) = (A × B) ∪ (A × C)`.
 -/
@@ -539,7 +560,7 @@ theorem exercise_3_2a {A : Set α} {B C : Set β}
     _ = { p | p ∈ Set.prod A B ∨ (p ∈ Set.prod A C) } := rfl
     _ = (Set.prod A B) ∪ (Set.prod A C) := rfl
 
-/-- #### Exercise 3.2b
+/-- ### Exercise 3.2b
 
 Show that if `A × B = A × C` and `A ≠ ∅`, then `B = C`.
 -/
@@ -568,7 +589,7 @@ theorem exercise_3_2b {A : Set α} {B C : Set β}
     have ⟨c, hc⟩ := Set.nonempty_iff_ne_empty.mpr (Ne.symm nC)
     exact (h (a, c)).mpr ⟨ha, hc⟩
 
-/-- #### Exercise 3.3
+/-- ### Exercise 3.3
 
 Show that `A × ⋃ 𝓑 = ⋃ {A × X | X ∈ 𝓑}`.
 -/
@@ -596,7 +617,7 @@ theorem exercise_3_3 {A : Set (Set α)} {𝓑 : Set (Set β)}
       · intro ⟨b, h₁, h₂, h₃⟩
         exact ⟨b, h₁, h₂, h₃⟩
 
-/-- #### Exercise 3.5a
+/-- ### Exercise 3.5a
 
 Assume that `A` and `B` are given sets, and show that there exists a set `C`
 such that for any `y`,
@@ -664,7 +685,7 @@ theorem exercise_3_5a {A : Set α} {B : Set β}
         rw [hab.right]
         exact ⟨hab.left, hb⟩
 
-/-- #### Exercise 3.5b
+/-- ### Exercise 3.5b
 
 With `A`, `B`, and `C` as above, show that `A × B = ∪ C`.
 -/
@@ -697,7 +718,7 @@ theorem exercise_3_5b {A : Set α} (B : Set β)
     exact ⟨h, hb⟩
 
 
-/-- #### Exercise 3.6
+/-- ### Exercise 3.6
 
 Show that a set `A` is a relation **iff** `A ⊆ dom A × ran A`.
 -/
@@ -715,7 +736,7 @@ theorem exercise_3_6 {A : Set.HRelation α β}
   ]
   exact ⟨⟨b, ht⟩, ⟨a, ht⟩⟩
 
-/-- #### Exercise 3.7
+/-- ### Exercise 3.7
 
 Show that if `R` is a relation, then `fld R = ⋃ ⋃ R`.
 -/
@@ -794,7 +815,7 @@ theorem exercise_3_7 {R : Set.Relation α}
       simp only [Set.mem_singleton_iff, Set.mem_insert_iff] at this
       exact hxy_mem this
 
-/-- #### Exercise 3.8 (i)
+/-- ### Exercise 3.8 (i)
 
 Show that for any set `𝓐`:
 ```
@@ -820,7 +841,7 @@ theorem exercise_3_8_i {A : Set (Set.HRelation α β)}
   · intro ⟨t, ht, y, hx⟩
     exact ⟨y, t, ht, hx⟩
 
-/-- #### Exercise 3.8 (ii)
+/-- ### Exercise 3.8 (ii)
 
 Show that for any set `𝓐`:
 ```
@@ -845,7 +866,7 @@ theorem exercise_3_8_ii {A : Set (Set.HRelation α β)}
   · intro ⟨y, ⟨hy, ⟨t, ht⟩⟩⟩
     exact ⟨t, ⟨y, ⟨hy, ht⟩⟩⟩
 
-/-- #### Exercise 3.9 (i)
+/-- ### Exercise 3.9 (i)
 
 Discuss the result of replacing the union operation by the intersection
 operation in the preceding problem.
@@ -871,7 +892,7 @@ theorem exercise_3_9_i {A : Set (Set.HRelation α β)}
   intro _ y hy R hR
   exact ⟨y, hy R hR⟩
 
-/-- #### Exercise 3.9 (ii)
+/-- ### Exercise 3.9 (ii)
 
 Discuss the result of replacing the union operation by the intersection
 operation in the preceding problem.
@@ -897,7 +918,7 @@ theorem exercise_3_9_ii {A : Set (Set.HRelation α β)}
   intro _ y hy R hR
   exact ⟨y, hy R hR⟩
 
-/-- #### Exercise 3.12
+/-- ### Exercise 3.12
 
 Assume that `f` and `g` are functions and show that
 ```
@@ -927,7 +948,7 @@ theorem exercise_3_12 {f g : Set.HRelation α β}
     rw [single_valued_eq_unique hf hp hy₁.left.left]
     exact hy₁.left.right
 
-/-- #### Exercise 3.13
+/-- ### Exercise 3.13
 
 Assume that `f` and `g` are functions with `f ⊆ g` and `dom g ⊆ dom f`. Show
 that `f = g`.
@@ -951,7 +972,7 @@ theorem exercise_3_13 {f g : Set.HRelation α β}
     rw [single_valued_eq_unique hg hp hx.left.right]
     exact hx.left.left
 
-/-- #### Exercise 3.14 (a)
+/-- ### Exercise 3.14 (a)
 
 Assume that `f` and `g` are functions. Show that `f ∩ g` is a function.
 -/
@@ -960,7 +981,7 @@ theorem exercise_3_14_a {f g : Set.HRelation α β}
   : isSingleValued (f ∩ g) :=
   single_valued_subset hf (Set.inter_subset_left f g)
 
-/-- #### Exercise 3.14 (b)
+/-- ### Exercise 3.14 (b)
 
 Assume that `f` and `g` are functions. Show that `f ∪ g` is a function **iff**
 `f(x) = g(x)` for every `x` in `(dom f) ∩ (dom g)`.
@@ -1040,7 +1061,7 @@ theorem exercise_3_14_b {f g : Set.HRelation α β}
       · intro hz
         exact absurd (mem_pair_imp_fst_mem_dom hz) hgx
 
-/-- #### Exercise 3.15
+/-- ### Exercise 3.15
 
 Let `𝓐` be a set of functions such that for any `f` and `g` in `𝓐`, either
 `f ⊆ g` or `g ⊆ f`. Show that `⋃ 𝓐` is a function.
@@ -1063,7 +1084,7 @@ theorem exercise_3_15 {𝓐 : Set (Set.HRelation α β)}
     have := hg' hg.right
     exact single_valued_eq_unique (h𝓐 f hf.left) this hf.right
 
-/-! #### Exercise 3.17
+/-! ### Exercise 3.17
 
 Show that the composition of two single-rooted sets is again single-rooted.
 Conclude that the composition of two one-to-one functions is again one-to-one.
@@ -1073,7 +1094,7 @@ theorem exercise_3_17_i {F : Set.HRelation β γ} {G : Set.HRelation α β}
   (hF : isSingleRooted F) (hG : isSingleRooted G)
   : isSingleRooted (comp F G):= by
   intro v hv
-  
+
   have ⟨u₁, hu₁⟩ := ran_exists hv
   have hu₁' := hu₁
   unfold comp at hu₁'
@@ -1081,13 +1102,13 @@ theorem exercise_3_17_i {F : Set.HRelation β γ} {G : Set.HRelation α β}
   have ⟨t₁, ht₁⟩ := hu₁'
   unfold ExistsUnique
   refine ⟨u₁, ⟨mem_pair_imp_fst_mem_dom hu₁, hu₁⟩, ?_⟩
-  
+
   intro u₂ hu₂
   have hu₂' := hu₂
   unfold comp at hu₂'
   simp only [Set.mem_setOf_eq] at hu₂'
   have ⟨_, ⟨t₂, ht₂⟩⟩ := hu₂'
-  
+
   have ht : t₁ = t₂ := single_rooted_eq_unique hF ht₁.right ht₂.right
   rw [ht] at ht₁
   exact single_rooted_eq_unique hG ht₂.left ht₁.left
@@ -1098,7 +1119,7 @@ theorem exercise_3_17_ii {F : Set.HRelation β γ} {G : Set.HRelation α β}
       (single_valued_comp_is_single_valued hF.left hG.left)
       (exercise_3_17_i hF.right hG.right)
 
-/-! #### Exercise 3.18
+/-! ### Exercise 3.18
 
 Let `R` be the set
 ```
@@ -1231,7 +1252,7 @@ theorem exercise_3_18_v
 
 end Exercise_3_18
 
-/-! #### Exercise 3.19
+/-! ### Exercise 3.19
 
 Let
 ```
@@ -1435,7 +1456,7 @@ theorem exercise_3_19_x
     apply Or.elim ht₁
     · intro ht
       rw [← ht] at ht₂
-      simp only [Set.mem_singleton_iff, Set.mem_insert_iff] at ht₂ 
+      simp only [Set.mem_singleton_iff, Set.mem_insert_iff] at ht₂
       apply Or.elim ht₂
       · intro ha
         rw [ha] at hx
@@ -1481,7 +1502,7 @@ theorem exercise_3_19_x
 
 end Exercise_3_19
 
-/-- #### Exercise 3.20
+/-- ### Exercise 3.20
 
 Show that `F ↾ A = F ∩ (A × ran F)`.
 -/
@@ -1501,7 +1522,7 @@ theorem exercise_3_20 {F : Set.HRelation α β} {A : Set α}
     _ = F ∩ {p | p.fst ∈ A ∧ p.snd ∈ ran F} := rfl
     _ = F ∩ (Set.prod A (ran F)) := rfl
 
-/-- #### Exercise 3.22 (a)
+/-- ### Exercise 3.22 (a)
 
 Show that the following is correct for any sets.
 ```
@@ -1516,7 +1537,7 @@ theorem exercise_3_22_a {A B : Set α} {F : Set.HRelation α β} (h : A ⊆ B)
   have := h hu.left
   exact ⟨u, this, hu.right⟩
 
-/-- #### Exercise 3.22 (b)
+/-- ### Exercise 3.22 (b)
 
 Show that the following is correct for any sets.
 ```
@@ -1546,7 +1567,7 @@ theorem exercise_3_22_b {A B : Set α} {F : Set.HRelation α β}
     _ = { v | ∃ a ∈ image G A, (a, v) ∈ F } := rfl
     _ = image F (image G A) := rfl
 
-/-- #### Exercise 3.22 (c)
+/-- ### Exercise 3.22 (c)
 
 Show that the following is correct for any sets.
 ```
@@ -1564,7 +1585,7 @@ theorem exercise_3_22_c {A B : Set α} {Q : Set.Relation α}
     _ = { p | p ∈ Q ∧ p.1 ∈ A} ∪ { p | p ∈ Q ∧ p.1 ∈ B } := rfl
     _ = (restriction Q A) ∪ (restriction Q B) := rfl
 
-/-- #### Exercise 3.23 (i)
+/-- ### Exercise 3.23 (i)
 
 Let `I` be the identity function on the set `A`. Show that for any sets `B` and
 `C`, `B ∘ I = B ↾ A`.
@@ -1588,7 +1609,7 @@ theorem exercise_3_23_i {A : Set α} {B : Set.HRelation α β} {I : Set.Relation
     intro (x, y) hp
     refine ⟨x, ⟨hp.right, rfl⟩, hp.left⟩
 
-/-- #### Exercise 3.23 (ii)
+/-- ### Exercise 3.23 (ii)
 
 Let `I` be the identity function on the set `A`. Show that for any sets `B` and
 `C`, `I⟦C⟧ = A ∩ C`.
@@ -1620,7 +1641,7 @@ theorem exercise_3_23_ii {A C : Set α} {I : Set.Relation α}
     _ = C ∩ A := rfl
     _ = A ∩ C := Set.inter_comm C A
 
-/-- #### Exercise 3.24
+/-- ### Exercise 3.24
 
 Show that for a function `F`, `F⁻¹⟦A⟧ = { x ∈ dom F | F(x) ∈ A }`.
 -/
@@ -1650,7 +1671,7 @@ theorem exercise_3_24 {F : Set.HRelation α β} {A : Set β}
       · intro ⟨y, hy⟩
         exact ⟨y, hy.left⟩
 
-/-- #### Exercise 3.25 (b)
+/-- ### Exercise 3.25 (b)
 
 Show that the result of part (a) holds for any function `G`, not necessarily
 one-to-one.
@@ -1673,7 +1694,7 @@ theorem exercise_3_25_b {G : Set.HRelation α β} (hG : isSingleValued G)
     have ⟨t, ht⟩ := ran_exists h.left
     exact ⟨t, ⟨t, x, ht, rfl, rfl⟩, by rwa [← h.right]⟩
 
-/-- #### Exercise 3.25 (a)
+/-- ### Exercise 3.25 (a)
 
 Assume that `G` is a one-to-one function. Show that `G ∘ G⁻¹` is the identity
 function on `ran G`.
@@ -1682,7 +1703,7 @@ theorem exercise_3_25_a {G : Set.HRelation α β} (hG : isOneToOne G)
   : comp G (inv G) = { p | p.1 ∈ ran G ∧ p.1 = p.2 } :=
   exercise_3_25_b hG.left
 
-/-- #### Exercise 3.27
+/-- ### Exercise 3.27
 
 Show that `dom (F ∘ G) = G⁻¹⟦dom F⟧` for any sets `F` and `G`. (`F` and `G` need
 not be functions.)
@@ -1716,7 +1737,7 @@ theorem exercise_3_27 {F : Set.HRelation β γ} {G : Set.HRelation α β}
     ]
     exact ⟨t, u, hu.right, ht⟩
 
-/-- #### Exercise 3.28
+/-- ### Exercise 3.28
 
 Assume that `f` is a one-to-one function from `A` into `B`, and that `G` is the
 function with `dom G = 𝒫 A` defined by the equation `G(X) = f⟦X⟧`. Show that `G`
@@ -1780,7 +1801,7 @@ theorem exercise_3_28 {A : Set α} {B : Set β}
       have hX₁sub := mem_pair_imp_fst_mem_dom hX₁
       rw [dG] at hX₁sub
       simp only [Set.mem_powerset_iff] at hX₁sub
-      
+
       have ht' := hX₁sub ht
       rw [← hf.right.dom_eq] at ht'
       have ⟨ft, hft⟩ := dom_exists ht'
@@ -1811,7 +1832,7 @@ theorem exercise_3_28 {A : Set α} {B : Set β}
     have hz := mem_pair_imp_snd_mem_ran hb.right
     exact hf.right.ran_ss hz
 
-/-- #### Exercise 3.29
+/-- ### Exercise 3.29
 
 Assume that `f : A → B` and define a function `G : B → 𝒫 A` by
 ```
@@ -1854,7 +1875,7 @@ theorem exercise_3_29 {f : Set.HRelation α β} {G : Set.HRelation β (Set α)}
   rw [heq] at this
   exact single_valued_eq_unique hf.is_func this.right ht
 
-/-! #### Exercise 3.30
+/-! ### Exercise 3.30
 
 Assume that `F : 𝒫 A → 𝒫 A` and that `F` has the monotonicity property:
 ```
@@ -1871,7 +1892,7 @@ variable {F : Set α → Set α} {A B C : Set α}
          (hB : B = ⋂₀ { X | X ⊆ A ∧ F X ⊆ X })
          (hC : C = ⋃₀ { X | X ⊆ A ∧ X ⊆ F X })
 
-/-- ##### Exercise 3.30 (a)
+/-- #### Exercise 3.30 (a)
 
 Show that `F(B) = B` and `F(C) = C`.
 -/
@@ -1885,12 +1906,12 @@ theorem exercise_3_30_a : F B = B ∧ F C = C := by
         show ∀ t, t ∈ B → t ∈ X
         intro t ht
         rw [hB] at ht
-        simp only [Set.mem_sInter] at ht 
+        simp only [Set.mem_sInter] at ht
         exact ht X ⟨hX₁, hX₂⟩
       exact hX₂ (hMono B X ⟨hB₁, hX₁⟩ hx)
     rw [hB]
     exact this
-  
+
   have hC_supset : C ⊆ F C := by
     intro x hx
     rw [hC] at hx
@@ -1910,7 +1931,7 @@ theorem exercise_3_30_a : F B = B ∧ F C = C := by
       have ⟨T, hT⟩ := ht
       exact hT.left.left hT.right
     exact hMono X C ⟨hC₁, hC₂⟩ (hX.left.right hX.right)
-  
+
   have hC_sub_A : C ⊆ A := by
     show ∀ t, t ∈ C → t ∈ A
     intro t ht
@@ -1936,7 +1957,7 @@ theorem exercise_3_30_a : F B = B ∧ F C = C := by
     intro t ht
     simp only [Set.mem_sUnion, Set.mem_setOf_eq]
     exact ⟨X, hX, ht⟩
-  
+
   have hB_sub_A : B ⊆ A := by
     show ∀ t, t ∈ B → t ∈ A
     intro t ht
@@ -1951,11 +1972,11 @@ theorem exercise_3_30_a : F B = B ∧ F C = C := by
     · exact hB_subset
     · have hInter : ∀ X, X ∈ {X | X ⊆ A ∧ F X ⊆ X} → B ⊆ X := by
         intro X hX
-        simp only [Set.mem_setOf_eq] at hX 
+        simp only [Set.mem_setOf_eq] at hX
         rw [hB]
         show ∀ t, t ∈ ⋂₀ {X | X ⊆ A ∧ F X ⊆ X} → t ∈ X
         intro t ht
-        simp only [Set.mem_sInter, Set.mem_setOf_eq] at ht 
+        simp only [Set.mem_sInter, Set.mem_setOf_eq] at ht
         exact ht X hX
       refine hInter (F B) ⟨?_, ?_⟩
       · show ∀ t, t ∈ F B → t ∈ A
@@ -1967,7 +1988,7 @@ theorem exercise_3_30_a : F B = B ∧ F C = C := by
   · rw [Set.Subset.antisymm_iff]
     exact ⟨hC_subset, hC_supset⟩
 
-/-- ##### Exercise 3.30 (b)
+/-- #### Exercise 3.30 (b)
 
 Show that if `F(X) = X`, then `B ⊆ X ⊆ C`.
 -/
@@ -1978,7 +1999,7 @@ theorem exercise_3_30_b : ∀ X, X ⊆ A ∧ F X = X → B ⊆ X ∧ X ⊆ C :=
     rw [hB]
     show ∀ t, t ∈ ⋂₀ {X | X ⊆ A ∧ F X ⊆ X} → t ∈ X
     intro t ht
-    simp only [Set.mem_sInter, Set.mem_setOf_eq] at ht 
+    simp only [Set.mem_sInter, Set.mem_setOf_eq] at ht
     exact ht X ⟨hX₁, this⟩
   · have : X ⊆ F X := Eq.subset (id (Eq.symm hX₂))
     rw [hC]
@@ -1989,7 +2010,7 @@ theorem exercise_3_30_b : ∀ X, X ⊆ A ∧ F X = X → B ⊆ X ∧ X ⊆ C :=
 
 end Exercise_3_30
 
-/-- #### Exercise 3.32 (a)
+/-- ### Exercise 3.32 (a)
 
 Show that `R` is symmetric **iff** `R⁻¹ ⊆ R`.
 -/
@@ -2007,7 +2028,7 @@ theorem exercise_3_32_a {R : Set.Relation α}
     rw [← mem_self_comm_mem_inv] at hp
     exact hR hp
 
-/-- #### Exercise 3.32 (b)
+/-- ### Exercise 3.32 (b)
 
 Show that `R` is transitive **iff** `R ∘ R ⊆ R`.
 -/
@@ -2024,7 +2045,7 @@ theorem exercise_3_32_b {R : Set.Relation α}
     have : (x, z) ∈ comp R R := ⟨y, hx, hz⟩
     exact hR this
 
-/-- #### Exercise 3.33
+/-- ### Exercise 3.33
 
 Show that `R` is a symmetric and transitive relation **iff** `R = R⁻¹ ∘ R`.
 -/
@@ -2074,7 +2095,7 @@ theorem exercise_3_33 {R : Set.Relation α}
     rw [h, hR]
     exact ⟨y, hx, this⟩
 
-/-- #### Exercise 3.34 (a)
+/-- ### Exercise 3.34 (a)
 
 Assume that `𝓐` is a nonempty set, every member of which is a transitive
 relation. Is the set `⋂ 𝓐` a transitive relation?
@@ -2089,7 +2110,7 @@ theorem exercise_3_34_a {𝓐 : Set (Set.Relation α)}
   have hy' := hy A hA
   exact h𝓐 A hA hx' hy'
 
-/-- #### Exercise 3.34 (b)
+/-- ### Exercise 3.34 (b)
 
 Assume that `𝓐` is a nonempty set, every member of which is a transitive
 relation. Is `⋃ 𝓐` a transitive relation?
@@ -2136,7 +2157,7 @@ theorem exercise_3_34_b {𝓐 : Set (Set.Relation ℕ)}
         simp at this
     exact absurd (h h₁ h₂) h₃
 
-/-- #### Exercise 3.35
+/-- ### Exercise 3.35
 
 Show that for any `R` and `x`, we have `[x]_R = R⟦{x}⟧`.
 -/
@@ -2147,7 +2168,7 @@ theorem exercise_3_35 {R : Set.Relation α} {x : α}
     _ = { t | ∃ u ∈ ({x} : Set α), (u, t) ∈ R } := by simp
     _ = image R {x} := rfl
 
-/-- #### Exercise 3.36
+/-- ### Exercise 3.36
 
 Assume that `f : A → B` and that `R` is an equivalence relation on `B`. Define
 `Q` to be the set `{⟨x, y⟩ ∈ A × A | ⟨f(x), f(y)⟩ ∈ R}`. Show that `Q` is an
@@ -2173,7 +2194,7 @@ theorem exercise_3_36 {f : Set.HRelation α β}
       Prod.exists,
       exists_and_right,
       exists_eq_right
-    ] at hx 
+    ] at hx
     apply Or.elim hx
     · intro ⟨_, _, hx₁⟩
       rw [← hf.dom_eq]
@@ -2213,7 +2234,7 @@ theorem exercise_3_36 {f : Set.HRelation α β}
     simp only [exists_and_left, Set.mem_setOf_eq]
     exact ⟨fx, hfx, fz, hfz, hR.trans h₁ h₂⟩
 
-/-- #### Exercise 3.37
+/-- ### Exercise 3.37
 
 Assume that `P` is a partition of a set `A`. Define the relation `Rₚ` as
 follows:
@@ -2290,7 +2311,7 @@ theorem exercise_3_37 {P : Set (Set α)} {A : Set α}
     simp only [Set.mem_setOf_eq]
     exact ⟨B₁, hB₁.left, hB₁.right.left, by rw [hB]; exact hB₂.right.right⟩
 
-/-- #### Exercise 3.38
+/-- ### Exercise 3.38
 
 Theorem 3P shows that `A / R` is a partition of `A` whenever `R` is an
 equivalence relation on `A`. Show that if we start with the equivalence relation
@@ -2358,7 +2379,7 @@ theorem exercise_3_38 {P : Set (Set α)} {A : Set α}
         simp only [Set.mem_setOf_eq]
       _ = neighborhood Rₚ x := rfl
 
-/-- #### Exercise 3.39
+/-- ### Exercise 3.39
 
 Assume that we start with an equivalence relation `R` on `A` and define `P` to
 be the partition `A / R`. Show that `Rₚ`, as defined in Exercise 37, is just
@@ -2396,7 +2417,7 @@ theorem exercise_3_39 {P : Set (Set α)} {R Rₚ : Set.Relation α} {A : Set α}
     rw [hP]
     exact ⟨x, hxA, rfl⟩
 
-/-- #### Exercise 3.41 (a)
+/-- ### Exercise 3.41 (a)
 
 Let `ℝ` be the set of real numbers and define the realtion `Q` on `ℝ × ℝ` by
 `⟨u, v⟩ Q ⟨x, y⟩` **iff** `u + y = x + v`. Show that `Q` is an equivalence
@@ -2449,7 +2470,7 @@ theorem exercise_3_41_a {Q : Set.Relation (ℝ × ℝ)}
     conv => right; rw [add_comm]
     exact this
 
-/-- #### Exercise 3.43
+/-- ### Exercise 3.43
 
 Assume that `R` is a linear ordering on a set `A`. Show that `R⁻¹` is also a
 linear ordering on `A`.
@@ -2472,7 +2493,7 @@ theorem exercise_3_43 {R : Rel α α} (hR : IsStrictTotalOrder α R)
     unfold Rel.inv flip at *
     exact hR.trans c b a hac hab
 
-/-! #### Exercise 3.44
+/-! ### Exercise 3.44
 
 Assume that `<` is a linear ordering on a set `A`. Assume that `f : A → A` and
 that `f` has the property that whenever `x < y`, then `f(x) < f(y)`. Show that
@@ -2516,7 +2537,7 @@ theorem exercise_3_44_ii {R : Rel α α} (hR : IsStrictTotalOrder α R)
       have := hR.trans (f x) (f y) (f x) h (hf y x h₂)
       exact absurd this (hR.irrefl (f x))
 
-/-- #### Exercise 3.45
+/-- ### Exercise 3.45
 
 Assume that `<_A` and `<_B` are linear orderings on `A` and `B`, respectively.
 Define the binary relation `<_L` on the Cartesian product `A × B` by:
@@ -2595,4 +2616,4 @@ theorem exercise_3_45 {A : Rel α α} {B : Rel β β} {R : Rel (α × β) (α ×
         have := hB.trans b₁ b₂ b₃ ha₁.right hb₂
         exact (hR a₁ b₁ a₃ b₃).mpr (Or.inr ⟨ha₂, this⟩)
 
-end Enderton.Set.Chapter_3
+end Enderton.Set.Chapter_3

Bookshelf/Enderton/Set/Chapter_4.lean

@@ -11,7 +11,7 @@ Natural Numbers
 
 namespace Enderton.Set.Chapter_4
 
-/-- #### Theorem 4C
+/-- ### Theorem 4C
 
 Every natural number except `0` is the successor of some natural number.
 -/
@@ -23,7 +23,7 @@ theorem theorem_4c (n : ℕ)
 
 #check Nat.exists_eq_succ_of_ne_zero
 
-/-- #### Theorem 4I
+/-- ### Theorem 4I
 
 For natural numbers `m` and `n`,
 ```
@@ -34,7 +34,7 @@ m + n⁺ = (m + n)⁺
 theorem theorem_4i (m n : ℕ)
   : m + 0 = m ∧ m + n.succ = (m + n).succ := ⟨rfl, rfl⟩
 
-/-- #### Theorem 4J
+/-- ### Theorem 4J
 
 For natural numbers `m` and `n`,
 ```
@@ -45,7 +45,7 @@ m ⬝ n⁺ = m ⬝ n + m .
 theorem theorem_4j (m n : ℕ)
   : m * 0 = 0 ∧ m * n.succ = m * n + m := ⟨rfl, rfl⟩
 
-/-- #### Left Additive Identity
+/-- ### Left Additive Identity
 
 For all `n ∈ ω`, `A₀(n) = n`. In other words, `0 + n = n`.
 -/
@@ -60,7 +60,7 @@ lemma left_additive_identity (n : ℕ)
 
 #check Nat.zero_add
 
-/-- #### Lemma 2
+/-- ### Lemma 2
 
 For all `m, n ∈ ω`, `Aₘ₊(n) = Aₘ(n⁺)`. In other words, `m⁺ + n = m + n⁺`.
 -/
@@ -76,7 +76,7 @@ lemma lemma_2 (m n : ℕ)
 
 #check Nat.succ_add_eq_succ_add
 
-/-- #### Theorem 4K-1
+/-- ### Theorem 4K-1
 
 Associatve law for addition. For `m, n, p ∈ ω`,
 ```
@@ -99,7 +99,7 @@ theorem theorem_4k_1 {m n p : ℕ}
 
 #check Nat.add_assoc
 
-/-- #### Theorem 4K-2
+/-- ### Theorem 4K-2
 
 Commutative law for addition. For `m, n ∈ ω`,
 ```
@@ -119,7 +119,7 @@ theorem theorem_4k_2 {m n : ℕ}
 
 #check Nat.add_comm
 
-/-- #### Zero Multiplicand
+/-- ### Zero Multiplicand
 
 For all `n ∈ ω`, `M₀(n) = 0`. In other words, `0 ⬝ n = 0`.
 -/
@@ -135,7 +135,7 @@ theorem zero_multiplicand (n : ℕ)
 
 #check Nat.zero_mul
 
-/-- #### Successor Distribution
+/-- ### Successor Distribution
 
 For all `m, n ∈ ω`, `Mₘ₊(n) = Mₘ(n) + n`. In other words,
 ```
@@ -159,7 +159,7 @@ theorem succ_distrib (m n : ℕ)
 
 #check Nat.succ_mul
 
-/-- #### Theorem 4K-3
+/-- ### Theorem 4K-3
 
 Distributive law. For `m, n, p ∈ ω`,
 ```
@@ -181,7 +181,7 @@ theorem theorem_4k_3 (m n p : ℕ)
     _ = (m * n + n) + (m * p + p) := by rw [theorem_4k_1, theorem_4k_1]
     _ = m.succ * n + m.succ * p := by rw [succ_distrib, succ_distrib]
 
-/-- #### Successor Identity
+/-- ### Successor Identity
 
 For all `m ∈ ω`, `Aₘ(1) = m⁺`. In other words, `m + 1 = m⁺`.
 -/
@@ -197,7 +197,7 @@ theorem succ_identity (m : ℕ)
 
 #check Nat.succ_eq_one_add
 
-/-- #### Right Multiplicative Identity
+/-- ### Right Multiplicative Identity
 
 For all `m ∈ ω`, `Mₘ(1) = m`. In other words, `m ⬝ 1 = m`.
 -/
@@ -213,9 +213,9 @@ theorem right_mul_id (m : ℕ)
 
 #check Nat.mul_one
 
-/-- #### Theorem 4K-5
+/-- ### Theorem 4K-5
 
-Commutative law for multiplication. For `m, n ∈ ω`, `m ⬝ n = n ⬝ m`. 
+Commutative law for multiplication. For `m, n ∈ ω`, `m ⬝ n = n ⬝ m`.
 -/
 theorem theorem_4k_5 (m n : ℕ)
   : m * n = n * m := by
@@ -232,7 +232,7 @@ theorem theorem_4k_5 (m n : ℕ)
 
 #check Nat.mul_comm
 
-/-- #### Theorem 4K-4
+/-- ### Theorem 4K-4
 
 Associative law for multiplication. For `m, n, p ∈ ω`,
 ```
@@ -254,7 +254,7 @@ theorem theorem_4k_4 (m n p : ℕ)
 
 #check Nat.mul_assoc
 
-/-- #### Lemma 4L(b)
+/-- ### Lemma 4L(b)
 
 No natural number is a member of itself.
 -/
@@ -269,7 +269,7 @@ lemma lemma_4l_b (n : ℕ)
 
 #check Nat.lt_irrefl
 
-/-- #### Lemma 10
+/-- ### Lemma 10
 
 For every natural number `n ≠ 0`, `0 ∈ n`.
 -/
@@ -285,7 +285,7 @@ theorem zero_least_nat (n : ℕ)
 
 #check Nat.pos_of_ne_zero
 
-/-! #### Theorem 4N
+/-! ### Theorem 4N
 
 For any natural numbers `n`, `m`, and `p`,
 ```
@@ -299,9 +299,25 @@ m ∈ n ↔ m ⬝ p ∈ n ⬝ p.
 
 theorem theorem_4n_i (m n p : ℕ)
   : m < n ↔ m + p < n + p := by
+/-
+> Let `m` and `n` be natural numbers.
+>
+> ##### (⇒)
+> Suppose `m ∈ n`. Let
+>
+> `S = {p ∈ ω | m + p ∈ n + p}`
+-/
   have hf : ∀ m n : ℕ, m < n → m + p < n + p := by
     induction p with
+/-
+> It trivially follows that `0 ∈ S`.
+-/
     | zero => simp
+/-
+> Next, suppose `p ∈ S`. That is, suppose `m + p ∈ n + p`. By *Lemma 4L(a)*,
+> this holds if and only if `(m + p)⁺ ∈ (n + p)⁺`. *Theorem 4I* then implies
+> that `m + p⁺ ∈ n + p⁺` meaning `p⁺ ∈ S`.
+-/
     | succ p ih =>
       intro m n hp
       have := ih m n hp
@@ -310,29 +326,76 @@ theorem theorem_4n_i (m n p : ℕ)
       have h₂ : (n + p).succ = n + p.succ := rfl
       rwa [← h₁, ← h₂]
   apply Iff.intro
+/-
+> Thus `S` is an inductive set. Hence *Theorem 4B* implies `S = ω`. Therefore,
+> for all `p ∈ ω`, `m ∈n` implies `m + p ∈ n + p`.
+-/
   · exact hf m n
+/-
+> ##### (⇐)
+> Let `p` be a natural number and suppose `m + p ∈ n + p`. By the
+> *Trichotomy Law for `ω`*, there are two cases to consider regarding how `m`
+> and `n` relate to one another:
+-/
   · intro h
     match @trichotomous ℕ LT.lt _ m n with
-    | Or.inl h₁ =>
-      exact h₁
     | Or.inr (Or.inl h₁) =>
+/-
+> ###### Case 1
+> Suppose `m = n`. Then `m + p ∈ n + p = m + p`. *Lemma 4L(b)* shows this is
+> impossible.
+-/
       rw [← h₁] at h
       exact absurd h (lemma_4l_b (m + p))
     | Or.inr (Or.inr h₁) =>
+/-
+> ###### Case 2
+> Suppose `n ∈ m`. Then *(⇒)* indicates `n + p ∈ m + p`. But this contradicts
+> the *Trichotomy Law for `ω`* since, by hypothesis, `m + p ∈ n + p`.
+-/
       have := hf n m h₁
       exact absurd this (Nat.lt_asymm h)
+    | Or.inl h₁ =>
+/-
+> ###### Conclusion
+> By trichotomy, it follows `m ∈ n`.
+-/
+      exact h₁
 
 #check Nat.add_lt_add_iff_right
 
 theorem theorem_4n_ii (m n p : ℕ)
   : m < n ↔ m * p.succ < n * p.succ := by
+/-
+> Let `m` and `n` be natural numbers.
+>
+> ##### (⇒)
+> Suppose `m ∈ n`. Let
+>
+> `S = {p ∈ ω | m ⬝ p⁺ ∈ n ⬝ p⁺}`.
+-/
   have hf : ∀ m n : ℕ, m < n → m * p.succ < n * p.succ := by
     intro m n hp₁
     induction p with
     | zero =>
+/-
+> `0 ∈ S` by *Right Multiplicative Identity*.
+-/
       simp only [Nat.mul_one]
       exact hp₁
     | succ p ih =>
+/-
+> Next, suppose `p ∈ S`. That is, `m ⬝ p⁺ ∈ n ⬝ p⁺`. Then
+>
+> `m ⬝ p⁺⁺ = m ⬝ p⁺ + m` *Theorem 4J*
+>       ` ∈ n ⬝ p⁺ + m` *(i)*
+>       ` = m + n ⬝ p⁺` *Theorem 4K-2*
+>       ` ∈ n + n ⬝ p⁺` *(i)*
+>       ` = n ⬝p⁺ + n`  *Theorem 4K-2*
+>       ` n ⬝ p⁺⁺`      *Theorem 4J*
+>
+> Therefore `p⁺ ∈ S`.
+-/
       have hp₂ : m * p.succ < n * p.succ := by
         by_cases hp₃ : p = 0
         · rw [hp₃] at *
@@ -347,21 +410,47 @@ theorem theorem_4n_ii (m n p : ℕ)
         _ = n * p.succ + n := by rw [theorem_4k_2]
         _ = n * p.succ.succ := rfl
   apply Iff.intro
+/-
+> Thus `S` is an inductive set. Hence *Theorem 4B* implies `S = ω`. By
+> *Theorem 4C*, every natural number except `0` is the successor of some natural
+> number. Therefore, for all `p ∈ ω` such that `p ≠ 0`, `m ∈ n` implies
+`m ⬝ p ∈ n ⬝ p`.
+-/
   · exact hf m n
-  · intro hp
-    match @trichotomous ℕ LT.lt _ m n with
-    | Or.inl h₁ =>
-      exact h₁
-    | Or.inr (Or.inl h₁) =>
-      rw [← h₁] at hp
-      exact absurd hp (lemma_4l_b (m * p.succ))
-    | Or.inr (Or.inr h₁) =>
-      have := hf n m h₁
-      exact absurd this (Nat.lt_asymm hp)
+/-
+> ##### (⇐)
+> Let `p ≠ 0` be a natural number and suppose `m ⬝ p ∈ n ⬝ p`. By the
+> *Trichotomy Law for `ω`*, there are two cases to consider regarding how `m`
+> and `n` relate to one another.
+-/
+  intro hp
+  match @trichotomous ℕ LT.lt _ m n with
+  | Or.inr (Or.inl h₁) =>
+/-
+> ###### Case 1
+> Suppose `m = n`. Then `m ⬝ p ∈ n ⬝ p = m ⬝ p`. *Lemma 4L(b)* shows this is
+> impossible.
+-/
+    rw [← h₁] at hp
+    exact absurd hp (lemma_4l_b (m * p.succ))
+  | Or.inr (Or.inr h₁) =>
+/-
+> ###### Case 2
+> Suppose `n ∈ m`. Then *(⇒)* indicates `n ⬝ p ∈ m ⬝ p`. But this contradicts
+> *Trichotomy Law for `ω`* since, by hypothesis, `m ⬝ p ∈ n ⬝ p`.
+-/
+    have := hf n m h₁
+    exact absurd this (Nat.lt_asymm hp)
+  | Or.inl h₁ =>
+/-
+> ###### Conclusion
+> By trichotomy, it follows `m ∈ n`.
+-/
+    exact h₁
 
 #check Nat.mul_lt_mul_of_pos_right
 
-/-! #### Corollary 4P
+/-! ### Corollary 4P
 
 The following cancellation laws hold for `m`, `n`, and `p` in `ω`:
 ```
@@ -372,44 +461,87 @@ m ⬝ p = n ⬝ p ∧ p ≠ 0 ⇒ m = n.
 
 theorem corollary_4p_i (m n p : ℕ) (h : m + p = n + p)
   : m = n := by
+/-
+> Suppose `m + p = n + p`. By the *Trichotomy Law for `ω`*, there are two cases
+> to consider regarding how `m` and `n` relate to one another.
+-/
   match @trichotomous ℕ LT.lt _ m n with
   | Or.inl h₁ =>
+/-
+> If `m ∈n`, then *Theorem 4N* implies `m + p ∈ n + p`.
+-/
     rw [theorem_4n_i m n p, h] at h₁
     exact absurd h₁ (lemma_4l_b (n + p))
-  | Or.inr (Or.inl h₁) =>
-    exact h₁
   | Or.inr (Or.inr h₁) =>
+/-
+> If `n ∈ m`, then *Theorem 4N* implies `n + p ∈ m + p`.
+-/
     rw [theorem_4n_i n m p, h] at h₁
     exact absurd h₁ (lemma_4l_b (n + p))
+/-
+> Both of these contradict the *Trichotomy Law for `ω`* of `m + p` and `n + p`.
+> Thus `m = n` is the only remaining possibility.
+-/
+  | Or.inr (Or.inl h₁) =>
+    exact h₁
+
 
 #check Nat.add_right_cancel
 
-/-- #### Well Ordering of ω
+/-- ### Well Ordering of ω
 
 Let `A` be a nonempty subset of `ω`. Then there is some `m ∈ A` such that
 `m ≤ n` for all `n ∈ A`.
 -/
 theorem well_ordering_nat {A : Set ℕ} (hA : Set.Nonempty A)
   : ∃ m ∈ A, ∀ n, n ∈ A → m ≤ n := by
-  -- Assume `A` does not have a least element.
+/-
+> Let `A` be a nonempty subset of `ω`. For the sake of contradiciton, suppose
+> `A` does not have a least element.
+-/
   by_contra nh
   simp only [not_exists, not_and, not_forall, not_le, exists_prop] at nh
-
-  -- If we show the complement of `A` is `ω`, then `A = ∅`, a contradiction.
+/-
+> It then suffices to prove that the complement of `A` equals `ω`. If we do so,
+> then `A = ∅`, a contradiction.
+-/
   suffices A.compl = Set.univ by
     have h := Set.univ_diff_compl_eq_self A
     rw [this] at h
     simp only [sdiff_self, Set.bot_eq_empty] at h
     exact absurd h.symm (Set.Nonempty.ne_empty hA)
-  
-  -- Use strong induction to prove every element of `ω` is in the complement.
+/-
+> Define
+>
+> `S = {n ∈ ω | (∀ m ∈ n)m ∉ A}`.
+>
+> We prove `S` is an inductive set by showing that (i) `0 ∈ S` and (ii) if
+> `n ∈ S`, then `n⁺ ∈ S`. Afterward we show that `ω - A = ω`, completing the
+> proof.
+-/
   have : ∀ n : ℕ, (∀ m, m < n → m ∈ A.compl) := by
     intro n
     induction n with
     | zero =>
+/-
+> #### (i)
+> It vacuously holds that `0 ∈ S`.
+-/
       intro m hm
       exact False.elim (Nat.not_lt_zero m hm)
     | succ n ih =>
+/-
+> #### (ii)
+> Suppose `n ∈ S`. We want to prove that
+>
+> `∀ m, m ∈ n⁺ ⇒ m ∉ A`.
+>
+> To this end, let `m ∈ ω` such that `m ∈ n⁺`. By definition of the successor,
+> `m ∈ n` or `m = n`. If the former, `n ∈ S` implies `m ∉ A`. If the latter, it
+> isn't possible for `n ∈ A` since the *Trichotomy Law for `ω`* would otherwise
+> imply `n` is the least element of `A`, which is assumed to not exist. Hence
+> `n⁺ ∈ S`.
+-/
       intro m hm
       have hm' : m < n ∨ m = n := by
         rw [Nat.lt_succ] at hm
@@ -429,7 +561,12 @@ theorem well_ordering_nat {A : Set ℕ} (hA : Set.Nonempty A)
           exact absurd hp.left (ih p hp.right)
         · rw [h]
           exact hn
-
+/-
+> #### Conclusion
+> By *(i)* and *(ii)*, `S` is an inductive set. Since `S ⊆ ω`, *Theorem 4B*
+> implies `S = ω`. Bu this immediately implies `ω = ω - A` meaning `A` is the
+> empty set.
+-/
   ext x
   simp only [Set.mem_univ, iff_true]
   by_contra nh'
@@ -438,7 +575,7 @@ theorem well_ordering_nat {A : Set ℕ} (hA : Set.Nonempty A)
 
 #check WellOrder
 
-/-- #### Strong Induction Principle for ω
+/-- ### Strong Induction Principle for ω
 
 Let `A` be a subset of `ω`, and assume that for every `n ∈ ω`, if every number
 less than `n` is in `A`, then `n ∈ A`. Then `A = ω`.
@@ -451,25 +588,31 @@ theorem strong_induction_principle_nat (A : Set ℕ)
     rw [this] at h'
     simp only [Set.diff_empty] at h'
     exact h'.symm
-
+/-
+> For the sake of contradiction, suppose `ω - A` is a nonempty set. By
+> *Well Ordering of `ω`*, there exists a least element `m ∈ ω - A`.
+-/
   by_contra nh
   have ⟨m, hm⟩ := well_ordering_nat (Set.nmem_singleton_empty.mp nh)
   refine absurd (h m ?_) hm.left
-  
+/-
+> Then every number less than `m` is in `A`. But then *(4.23)* implies `m ∈ A`,
+> a contradiction. Thus `ω - A` is an empty set meaning `A = ω`.
+-/
   -- Show that every number less than `m` is in `A`.
   intro x hx
   by_contra nx
   have : x < x := Nat.lt_of_lt_of_le hx (hm.right x nx)
   simp at this
 
-/-- #### Exercise 4.1
+/-- ### Exercise 4.1
 
 Show that `1 ≠ 3` i.e., that `∅⁺ ≠ ∅⁺⁺⁺`.
 -/
 theorem exercise_4_1 : 1 ≠ 3 := by
   simp
 
-/-- #### Exercise 4.13
+/-- ### Exercise 4.13
 
 Let `m` and `n` be natural numbers such that `m ⬝ n = 0`. Show that either
 `m = 0` or `n = 0`.
@@ -498,7 +641,7 @@ Call a natural number *odd* if it has the form `(2 ⬝ p) + 1` for some `p`.
 -/
 def odd (n : ℕ) : Prop := ∃ p, (2 * p) + 1 = n
 
-/-- #### Exercise 4.14
+/-- ### Exercise 4.14
 
 Show that each natural number is either even or odd, but never both.
 -/
@@ -549,7 +692,7 @@ theorem exercise_4_14 (n : ℕ)
       have : even n := ⟨q, hq'⟩
       exact absurd this h
 
-/-- #### Exercise 4.17
+/-- ### Exercise 4.17
 
 Prove that `mⁿ⁺ᵖ = mⁿ ⬝ mᵖ.`
 -/
@@ -559,7 +702,7 @@ theorem exercise_4_17 (m n p : ℕ)
   | zero => calc m ^ (n + 0)
     _ = m ^ n := rfl
     _ = m ^ n * 1 := by rw [right_mul_id]
-    _ = m ^ n * m ^ 0 := rfl
+    _ = m ^ n * m ^ 0 := by rfl
   | succ p ih => calc m ^ (n + p.succ)
     _ = m ^ (n + p).succ := rfl
     _ = m ^ (n + p) * m := rfl
@@ -567,7 +710,7 @@ theorem exercise_4_17 (m n p : ℕ)
     _ = m ^ n * (m ^ p * m) := by rw [theorem_4k_4]
     _ = m ^ n * m ^ p.succ := rfl
 
-/-- #### Exercise 4.19
+/-- ### Exercise 4.19
 
 Prove that if `m` is a natural number and `d` is a nonzero number, then there
 exist numbers `q` and `r` such that `m = (d ⬝ q) + r` and `r` is less than `d`.
@@ -600,7 +743,7 @@ theorem exercise_4_19 (m d : ℕ) (hd : d ≠ 0)
         _ < d := hr
       simp at this
 
-/-- #### Exercise 4.22
+/-- ### Exercise 4.22
 
 Show that for any natural numbers `m` and `p` we have `m ∈ m + p⁺`.
 -/
@@ -612,7 +755,7 @@ theorem exercise_4_22 (m p : ℕ)
     _ < m + p.succ := ih
     _ < m + p.succ.succ := Nat.lt.base (m + p.succ)
 
-/-- #### Exercise 4.23
+/-- ### Exercise 4.23
 
 Assume that `m` and `n` are natural numbers with `m` less than `n`. Show that
 there is some `p` in `ω` for which `m + p⁺ = n`. (It follows from this and the
@@ -637,7 +780,7 @@ theorem exercise_4_23 {m n : ℕ} (hm : m < n)
       refine ⟨0, ?_⟩
       rw [hm₁]
 
-/-- #### Exercise 4.24
+/-- ### Exercise 4.24
 
 Assume that `m + n = p + q`. Show that
 ```
@@ -660,7 +803,7 @@ theorem exercise_4_24 (m n p q : ℕ) (h : m + n = p + q)
     rw [← h] at hr
     exact (theorem_4n_i m p n).mpr hr
 
-/-- #### Exercise 4.25
+/-- ### Exercise 4.25
 
 Assume that `n ∈ m` and `q ∈ p`. Show that
 ```
@@ -685,4 +828,4 @@ theorem exercise_4_25 (m n p q : ℕ) (h₁ : n < m) (h₂ : q < p)
   conv at h₁ => right; rw [add_comm]
   exact h₁
 
-end Enderton.Set.Chapter_4
+end Enderton.Set.Chapter_4

Bookshelf/Enderton/Set/OrderedPair.lean

@@ -28,8 +28,7 @@ theorem ext_iff {x y u v : α}
     ] at hu huv
     apply Or.elim hu <;> apply Or.elim huv
 
-    · -- #### Case 1
-      -- `{u} = {x}` and `{u, v} = {x}`.
+    · -- `{u} = {x}` and `{u, v} = {x}`.
       intro huv_x hu_x
       rw [Set.singleton_eq_singleton_iff] at hu_x
       rw [hu_x] at huv_x
@@ -41,8 +40,7 @@ theorem ext_iff {x y u v : α}
       rw [← hx_v] at this
       exact ⟨hu_x.symm, this⟩
 
-    · -- #### Case 2
-      -- `{u} = {x}` and `{u, v} = {x, y}`.
+    · -- `{u} = {x}` and `{u, v} = {x, y}`.
       intro huv_xy hu_x
       rw [Set.singleton_eq_singleton_iff] at hu_x
       rw [hu_x] at huv_xy
@@ -58,8 +56,7 @@ theorem ext_iff {x y u v : α}
         ] at this
         exact ⟨hu_x.symm, Or.elim this (absurd ·.symm hx_v) (·.symm)⟩
 
-    · -- #### Case 3
-      -- `{u} = {x, y}` and `{u, v} = {x}`.
+    · -- `{u} = {x, y}` and `{u, v} = {x}`.
       intro huv_x hu_xy
       rw [Set.ext_iff] at huv_x hu_xy
       have hu_x := huv_x u
@@ -71,7 +68,7 @@ theorem ext_iff {x y u v : α}
         true_iff,
         or_true,
         iff_true
-      ] at hu_x hy_u 
+      ] at hu_x hy_u
       apply Or.elim huv
       · intro huv_x
         rw [← hu_x, Set.ext_iff] at huv_x
@@ -93,19 +90,18 @@ theorem ext_iff {x y u v : α}
         · intro hv_y
           exact ⟨hu_x.symm, hv_y.symm⟩
 
-    · -- #### Case 4
-      -- `{u} = {x, y}` and `{u, v} = {x, y}`.
+    · -- `{u} = {x, y}` and `{u, v} = {x, y}`.
       intro huv_xy hu_xy
       rw [Set.ext_iff] at huv_xy hu_xy
       have hx_u := hu_xy x
       have hy_u := hu_xy y
       simp only [
         Set.mem_singleton_iff, Set.mem_insert_iff, true_or, iff_true, or_true
-      ] at hx_u hy_u 
+      ] at hx_u hy_u
       have := huv_xy v
       simp only [
         Set.mem_singleton_iff, Set.mem_insert_iff, or_true, true_iff
-      ] at this 
+      ] at this
       apply Or.elim this
       · intro hv_x
         rw [hv_x, hx_u]
@@ -116,4 +112,4 @@ theorem ext_iff {x y u v : α}
   · intro h
     rw [h.left, h.right]
 
-end OrderedPair
+end OrderedPair

Bookshelf/Enderton/Set/Relation.lean

@@ -168,7 +168,7 @@ theorem ran_inv_eq_dom_self {F : HRelation α β}
 The restriction of a `Relation` to a `Set`.
 -/
 def restriction (R : HRelation α β) (A : Set α) : HRelation α β :=
-  { p ∈ R | p.1 ∈ A } 
+  { p ∈ R | p.1 ∈ A }
 
 /-! ## Image -/
 
@@ -580,7 +580,7 @@ theorem neighborhood_eq_iff_mem_relate {R : Set.Relation α} {A : Set α}
 
 /--
 Assume that `R` is an equivalence relation on `A`. If two sets `x` and `y`
-belong to the same neighborhood, then `xRy`. 
+belong to the same neighborhood, then `xRy`.
 -/
 theorem neighborhood_mem_imp_relate {R : Set.Relation α} {A : Set α}
   (hR : isEquivalence R A)
@@ -596,7 +596,7 @@ A **partition** `Π` of a set `A` is a set of nonempty subsets of `A` that is
 disjoint and exhaustive.
 -/
 structure Partition (P : Set (Set α)) (A : Set α) : Prop where
-  p_subset : ∀ p ∈ P, p ⊆ A 
+  p_subset : ∀ p ∈ P, p ⊆ A
   nonempty : ∀ p ∈ P, Set.Nonempty p
   disjoint : ∀ a ∈ P, ∀ b, b ∈ P → a ≠ b → a ∩ b = ∅
   exhaustive : ∀ a ∈ A, ∃ p, p ∈ P ∧ a ∈ p
@@ -666,4 +666,4 @@ theorem modEquiv_partition {A : Set α} {R : Relation α} (hR : isEquivalence R
 
 end Relation
 
-end Set
+end Set

Bookshelf/Fraleigh.lean

@@ -1 +1,10 @@
 import Bookshelf.Fraleigh.Chapter_1
+
+/-! # A First Course in Abstract Algebra
+
+## Fraleigh, John B.
+
+### Lean
+
+* [Chapter 1: Introduction and Examples](Bookshelf/Fraleigh/Chapter_1.html)
+-/

Bookshelf/Smullyan/Aviary.lean

@@ -9,7 +9,7 @@ considering they still have the same limitation described above during actual
 use. Their inclusion here serves more as pseudo-documentation than anything.
 -/
 
-/-- #### Bald Eagle
+/-- ### Bald Eagle
 
 `E'xy₁y₂y₃z₁z₂z₃ = x(y₁y₂y₃)(z₁z₂z₃)`
 -/
@@ -17,31 +17,31 @@ def E' (x : α → β → γ)
   (y₁ : δ → ε → α) (y₂ : δ) (y₃ : ε)
   (z₁ : ζ → η → β) (z₂ : ζ) (z₃ : η) := x (y₁ y₂ y₃) (z₁ z₂ z₃)
 
-/-- #### Becard
+/-- ### Becard
 
 `B₃xyzw = x(y(zw))`
 -/
 def B₃ (x : α → ε) (y : β → α) (z : γ → β) (w : γ) := x (y (z w))
 
-/-- #### Blackbird
+/-- ### Blackbird
 
 `B₁xyzw = x(yzw)`
 -/
 def B₁ (x : α → ε) (y : β → γ → α) (z : β) (w : γ) := x (y z w)
 
-/-- #### Bluebird
+/-- ### Bluebird
 
 `Bxyz = x(yz)`
 -/
 def B (x : α → γ) (y : β → α) (z : β) := x (y z)
 
-/-- #### Bunting
+/-- ### Bunting
 
 `B₂xyzwv = x(yzwv)`
 -/
 def B₂ (x : α → ζ) (y : β → γ → ε → α) (z : β) (w : γ) (v : ε) := x (y z w v)
 
-/-- #### Cardinal Once Removed
+/-- ### Cardinal Once Removed
 
 `C*xyzw = xywz`
 -/
@@ -49,48 +49,48 @@ def C_star (x : α → β → γ → δ) (y : α) (z : γ) (w : β) := x y w z
 
 notation "C*" => C_star
 
-/-- #### Cardinal
+/-- ### Cardinal
 
 `Cxyz = xzy`
 -/
 def C (x : α → β → δ) (y : β) (z : α) := x z y
 
-/-- #### Converse Warbler
+/-- ### Converse Warbler
 
 `W'xy = yxx`
 -/
 def W' (x : α) (y : α → α → β) := y x x
 
-/-- #### Dickcissel
+/-- ### Dickcissel
 
 `D₁xyzwv = xyz(wv)`
 -/
 def D₁ (x : α → β → δ → ε) (y : α) (z : β) (w : γ → δ) (v : γ) := x y z (w v)
 
-/-! #### Double Mockingbird
+/-! ### Double Mockingbird
 
 `M₂xy = xy(xy)`
 -/
 
-/-- #### Dove
+/-- ### Dove
 
 `Dxyzw = xy(zw)`
 -/
 def D (x : α → γ → δ) (y : α) (z : β → γ) (w : β) := x y (z w)
 
-/-- #### Dovekie
+/-- ### Dovekie
 
 `D₂xyzwv = x(yz)(wv)`
 -/
 def D₂ (x : α → δ → ε) (y : β → α) (z : β) (w : γ → δ) (v : γ) := x (y z) (w v)
 
-/-- #### Eagle
+/-- ### Eagle
 
 `Exyzwv = xy(zwv)`
 -/
 def E (x : α → δ → ε) (y : α) (z : β → γ → δ) (w : β) (v : γ) := x y (z w v)
 
-/-- #### Finch Once Removed
+/-- ### Finch Once Removed
 
 `F*xyzw = xwzy`
 -/
@@ -98,95 +98,95 @@ def F_star (x : α → β → γ → δ) (y : γ) (z : β) (w : α) := x w z y
 
 notation "F*" => F_star
 
-/-- #### Finch
+/-- ### Finch
 
 `Fxyz = zyx`
 -/
 def F (x : α) (y : β) (z : β → α → γ) := z y x
 
-/-- #### Goldfinch
+/-- ### Goldfinch
 
 `Gxyzw = xw(yz)`
 -/
 def G (x : α → γ → δ) (y : β → γ) (z : β) (w : α) := x w (y z)
 
-/-- #### Hummingbird
+/-- ### Hummingbird
 
 `Hxyz = xyzy`
 -/
 def H (x : α → β → α → γ) (y : α) (z : β) := x y z y
 
-/-- #### Identity Bird
+/-- ### Identity Bird
 
 `Ix = x`
 -/
 def I (x : α) : α := x
 
-/-- #### Kestrel
+/-- ### Kestrel
 
 `Kxy = x`
 -/
 def K (x : α) (_ : β) := x
 
-/-! #### Lark
+/-! ### Lark
 
 `Lxy = x(yy)`
 -/
 
-/-! #### Mockingbird
+/-! ### Mockingbird
 
 `Mx = xx`
 -/
 
-/-- #### Owl
+/-- ### Owl
 
 `Oxy = y(xy)`
 -/
 def O (x : (α → β) → α) (y : α → β) := y (x y)
 
-/-- #### Phoenix
+/-- ### Phoenix
 
 `Φxyzw = x(yw)(zw)`
 -/
 def Φ (x : β → γ → δ) (y : α → β) (z : α → γ) (w : α) := x (y w) (z w)
 
-/-- #### Psi Bird
+/-- ### Psi Bird
 
 `Ψxyzw = x(yz)(yw)`
 -/
 def Ψ (x : α → α → γ) (y : β → α) (z : β) (w : β) := x (y z) (y w)
 
-/-- #### Quacky Bird
+/-- ### Quacky Bird
 
 `Q₄xyz = z(yx)`
 -/
 def Q₄ (x : α) (y : α → β) (z : β → γ) := z (y x)
 
-/-- #### Queer Bird
+/-- ### Queer Bird
 
 `Qxyz = y(xz)`
 -/
 def Q (x : α → β) (y : β → γ) (z : α) := y (x z)
 
-/-- #### Quirky Bird
+/-- ### Quirky Bird
 
 `Q₃xyz = z(xy)`
 -/
 def Q₃ (x : α → β) (y : α) (z : β → γ) := z (x y)
 
-/-- #### Quixotic Bird
+/-- ### Quixotic Bird
 
 `Q₁xyz = x(zy)`
 -/
 def Q₁ (x : α → γ) (y : β) (z : β → α) := x (z y)
 
-/-- #### Quizzical Bird
+/-- ### Quizzical Bird
 
 `Q₂xyz = y(zx)`
 -/
 def Q₂ (x : α) (y : β → γ) (z : α → β) := y (z x)
 
-/-- #### Robin Once Removed
+/-- ### Robin Once Removed
 
 `R*xyzw = xzwy`
 -/
@@ -194,36 +194,36 @@ def R_star (x : α → β → γ → δ) (y : γ) (z : α) (w : β) := x z w y
 
 notation "R*" => R_star
 
-/-- #### Robin
+/-- ### Robin
 
 `Rxyz = yzx`
 -/
 def R (x : α) (y : β → α → γ) (z : β) := y z x
 
-/-- #### Sage Bird
+/-- ### Sage Bird
 
 `Θx = x(Θx)`
 -/
 partial def Θ [Inhabited α] (x : α → α) := x (Θ x)
 
-/-- #### Starling
+/-- ### Starling
 
 `Sxyz = xz(yz)`
 -/
 def S (x : α → β → γ) (y : α → β) (z : α) := x z (y z)
 
-/-- #### Thrush
+/-- ### Thrush
 
 `Txy = yx`
 -/
 def T (x : α) (y : α → β) := y x
 
-/-! #### Turing Bird
+/-! ### Turing Bird
 
 `Uxy = y(xxy)`
 -/
 
-/-- #### Vireo Once Removed
+/-- ### Vireo Once Removed
 
 `V*xyzw = xwyz`
 -/
@@ -231,13 +231,13 @@ def V_star (x : α → β → γ → δ) (y : β) (z : γ) (w : α) := x w y z
 
 notation "V*" => V_star
 
-/-- #### Vireo
+/-- ### Vireo
 
 `Vxyz = zxy`
 -/
 def V (x : α) (y : β) (z : α → β → γ) := z x y
 
-/-- #### Warbler
+/-- ### Warbler
 
 `Wxy = xyy`
 -/

Common/List/Basic.lean

@@ -162,7 +162,7 @@ theorem length_zipWith_self_tail_eq_length_sub_one
   rw [length_zipWith]
   simp only [length_cons, ge_iff_le, min_eq_right_iff]
   show length as ≤ length as + 1
-  simp only [le_add_iff_nonneg_right]
+  simp only [le_add_iff_nonneg_right, zero_le]
 
 /--
 The output `List` of a `zipWith` is nonempty **iff** both of its inputs are

Common/Logic/Basic.lean

@@ -1,4 +1,5 @@
 import Mathlib.Logic.Basic
+import Mathlib.Data.Set.Basic
 import Mathlib.Tactic.Tauto
 
 /-! # Common.Logic.Basic
@@ -39,4 +40,4 @@ theorem forall_mem_comm {X : Set α} {Y : Set β} (p : α → β → Prop)
   · intro h v hv u hu
     exact h u hu v hv
   · intro h u hu v hv
-    exact h v hv u hu
+    exact h v hv u hu

Common/Nat/Basic.lean

@@ -9,23 +9,4 @@ If `n < m⁺`, then `n < m` or `n = m`.
 theorem lt_or_eq_of_lt {n m : Nat} (h : n < m.succ) : n < m ∨ n = m :=
   lt_or_eq_of_le (lt_succ.mp h)
 
-/--
-The following cancellation law holds for `m`, `n`, and `p` in `ω`:
-```
-m ⬝ p = n ⬝ p ∧ p ≠ 0 → m = n
-```
--/
-theorem mul_right_cancel (m n p : ℕ) (hp : 0 < p) : m * p = n * p → m = n := by
-  intro hmn
-  match @trichotomous ℕ LT.lt _ m n with
-  | Or.inl h =>
-    have : m * p < n * p := Nat.mul_lt_mul_of_pos_right h hp
-    rw [hmn] at this
-    simp at this
-  | Or.inr (Or.inl h) => exact h
-  | Or.inr (Or.inr h) =>
-    have : n * p < m * p := Nat.mul_lt_mul_of_pos_right h hp
-    rw [hmn] at this
-    simp at this
-
-end Nat
+end Nat

Common/Real/Floor.lean

@@ -1,6 +1,5 @@
 import Mathlib.Algebra.BigOperators.Basic
-import Mathlib.Data.Real.Basic
-import Mathlib.Data.Finset.Basic
+import Mathlib.Data.Real.Archimedean
 
 /-! # Common.Real.Floor
 
@@ -145,4 +144,4 @@ theorem floor_mul_eq_sum_range_floor_add_index_div (n : ℕ) (x : ℝ)
   -- Close out goal by showing left- and right-hand side equal a common value.
   rw [hlhs, hrhs]
 
-end Real.Floor
+end Real.Floor

Common/Set.lean

@@ -1,4 +1,5 @@
 import Common.Set.Basic
 import Common.Set.Equinumerous
+import Common.Set.Function
 import Common.Set.Intervals
 import Common.Set.Peano

Common/Set/Basic.lean

@@ -193,6 +193,62 @@ theorem diff_ssubset_nonempty {A B : Set α} (h : A ⊂ B)
   · intro hx
     exact ⟨x, hx⟩
 
+/--
+If an element `x` is not a member of a set `A`, then `A - {x} = A`. 
+-/
+theorem not_mem_diff_eq_self {A : Set α} (h : a ∉ A)
+  : A \ {a} = A := by
+  ext x
+  apply Iff.intro
+  · exact And.left
+  · intro hx
+    refine ⟨hx, ?_⟩
+    simp only [mem_singleton_iff]
+    by_contra nx
+    rw [nx] at hx
+    exact absurd hx h
+
+/--
+Given two sets `A` and `B`, `(A - {a}) - (B - {b}) = (A - B) - {a}`.
+-/
+theorem diff_mem_diff_mem_eq_diff_diff_mem {A B : Set α} {a : α}
+  : (A \ {a}) \ (B \ {a}) = (A \ B) \ {a} := by
+  calc (A \ {a}) \ (B \ {a})
+    _ = { x | x ∈ A \ {a} ∧ x ∉ B \ {a} } := rfl
+    _ = { x | x ∈ A \ {a} ∧ ¬(x ∈ B \ {a}) } := rfl
+    _ = { x | (x ∈ A ∧ x ≠ a) ∧ ¬(x ∈ B ∧ x ≠ a) } := rfl
+    _ = { x | (x ∈ A ∧ x ≠ a) ∧ (x ∉ B ∨ x = a) } := by
+      ext x
+      rw [mem_setOf_eq, not_and_de_morgan]
+      simp
+    _ = { x | (x ∈ A ∧ x ≠ a ∧ x ∉ B) ∨ (x ∈ A ∧ x ≠ a ∧ x = a) } := by
+      ext x
+      simp only [mem_setOf_eq]
+      rw [and_or_left, and_assoc, and_assoc]
+    _ = { x | x ∈ A ∧ x ≠ a ∧ x ∉ B } := by simp
+    _ = { x | x ∈ A ∧ x ∉ B ∧ x ≠ a } := by
+      ext x
+      simp only [ne_eq, sep_and, mem_inter_iff, mem_setOf_eq]
+      apply Iff.intro <;>
+      · intro ⟨⟨_, hx₂⟩, hx₃, hx₄⟩
+        exact ⟨⟨hx₃, hx₄⟩, ⟨hx₃, hx₂⟩⟩
+    _ = { x | x ∈ A ∧ x ∉ B ∧ x ∉ ({a} : Set α) } := rfl
+    _ = { x | x ∈ A \ B ∧ x ∉ ({a} : Set α) } := by
+      ext x
+      simp only [
+        mem_singleton_iff,
+        sep_and,
+        mem_inter_iff,
+        mem_setOf_eq,
+        mem_diff,
+        and_congr_right_iff,
+        and_iff_right_iff_imp,
+        and_imp
+      ]
+      intro hx _ _
+      exact hx
+    _ = (A \ B) \ {a} := rfl
+
 /--
 For any set `A`, the difference between the sample space and `A` is the
 complement of `A`.

Common/Set/Equinumerous.lean

@@ -1,3 +1,5 @@
+import Common.Nat.Basic
+import Common.Set.Basic
 import Mathlib.Data.Finset.Card
 import Mathlib.Data.Set.Finite
 
@@ -8,6 +10,8 @@ Additional theorems around finite sets.
 
 namespace Set
 
+/-! ## Definitions -/
+
 /--
 A set `A` is equinumerous to a set `B` (written `A ≈ B`) if and only if there is
 a one-to-one function from `A` onto `B`.
@@ -19,6 +23,26 @@ infix:50 " ≈ " => Equinumerous
 theorem equinumerous_def (A : Set α) (B : Set β)
   : A ≈ B ↔ ∃ F, Set.BijOn F A B := Iff.rfl
 
+/--
+A set `A` is not equinumerous to a set `B` (written `A ≉ B`) if and only if
+there is no one-to-one function from `A` onto `B`.
+-/
+def NotEquinumerous (A : Set α) (B : Set β) : Prop := ¬ Equinumerous A B
+
+infix:50 " ≉ " => NotEquinumerous
+
+@[simp]
+theorem not_equinumerous_def : A ≉ B ↔ ∀ F, ¬ Set.BijOn F A B := by
+  apply Iff.intro
+  · intro h
+    unfold NotEquinumerous Equinumerous at h
+    simp only [not_exists] at h
+    exact h
+  · intro h
+    unfold NotEquinumerous Equinumerous
+    simp only [not_exists]
+    exact h
+
 /--
 For any set `A`, `A ≈ A`.
 -/
@@ -57,30 +81,131 @@ theorem eq_imp_equinumerous {A B : Set α} (h : A = B)
   conv at this => right; rw [h]
   exact this
 
+/-! ## Finite Sets -/
+
 /--
 A set is finite if and only if it is equinumerous to a natural number.
 -/
 axiom finite_iff_equinumerous_nat {α : Type _} {S : Set α}
   : Set.Finite S ↔ ∃ n : ℕ, S ≈ Set.Iio n
 
+/-! ## Emptyset -/
+
 /--
-A set `A` is not equinumerous to a set `B` (written `A ≉ B`) if and only if
-there is no one-to-one function from `A` onto `B`.
+Any set equinumerous to the emptyset is the emptyset.
 -/
-def NotEquinumerous (A : Set α) (B : Set β) : Prop := ¬ Equinumerous A B
-
-infix:50 " ≉ " => NotEquinumerous
-
 @[simp]
-theorem not_equinumerous_def : A ≉ B ↔ ∀ F, ¬ Set.BijOn F A B := by
+theorem equinumerous_zero_iff_emptyset {S : Set α}
+  : S ≈ Set.Iio 0 ↔ S = ∅ := by
   apply Iff.intro
+  · intro ⟨f, hf⟩
+    by_contra nh
+    rw [← Ne.def, ← Set.nonempty_iff_ne_empty] at nh
+    have ⟨x, hx⟩ := nh
+    have := hf.left hx
+    simp at this
   · intro h
-    unfold NotEquinumerous Equinumerous at h
-    simp only [not_exists] at h
-    exact h
-  · intro h
-    unfold NotEquinumerous Equinumerous
-    simp only [not_exists]
-    exact h
+    rw [h]
+    refine ⟨fun _ => ⊥, ?_, ?_, ?_⟩
+    · intro _ hx
+      simp at hx
+    · intro _ hx
+      simp at hx
+    · unfold SurjOn
+      simp only [bot_eq_zero', image_empty]
+      show ∀ x, x ∈ Set.Iio 0 → x ∈ ∅
+      intro _ hx
+      simp at hx
 
-end Set
+/--
+Empty sets are always equinumerous, regardless of their underlying type.
+-/
+theorem equinumerous_emptyset_emptyset [Bot β]
+  : (∅ : Set α) ≈ (∅ : Set β) := by
+  refine ⟨fun _ => ⊥, ?_, ?_, ?_⟩
+  · intro _ hx
+    simp at hx
+  · intro _ hx
+    simp at hx
+  · unfold SurjOn
+    simp
+
+/--
+For all natural numbers `m, n`, `m⁺ - n⁺ ≈ m - n`.
+-/
+theorem succ_diff_succ_equinumerous_diff {m n : ℕ}
+  : Set.Iio m.succ \ Set.Iio n.succ ≈ Set.Iio m \ Set.Iio n := by
+  refine Set.equinumerous_symm ⟨fun x => x + 1, ?_, ?_, ?_⟩
+  · intro x ⟨hx₁, hx₂⟩
+    simp at hx₁ hx₂ ⊢
+    exact ⟨Nat.le_add_of_sub_le hx₂, Nat.add_lt_of_lt_sub hx₁⟩
+  · intro _ _ _ _ h
+    simp only [add_left_inj] at h
+    exact h
+  · unfold Set.SurjOn Set.image
+    rw [Set.subset_def]
+    intro x ⟨hx₁, hx₂⟩
+    simp only [
+      Set.Iio_diff_Iio,
+      gt_iff_lt,
+      not_lt,
+      ge_iff_le,
+      Set.mem_setOf_eq,
+      Set.mem_Iio
+    ] at hx₁ hx₂ ⊢
+    have ⟨p, hp⟩ : ∃ p : ℕ, x = p.succ := by
+      refine Nat.exists_eq_succ_of_ne_zero ?_
+      have := calc 0
+        _ < n.succ := by simp
+        _ ≤ x := hx₂
+      exact Nat.pos_iff_ne_zero.mp this
+    refine ⟨p, ⟨?_, ?_⟩, hp.symm⟩
+    · rw [hp] at hx₂
+      exact Nat.lt_succ.mp hx₂
+    · rw [hp] at hx₁
+      exact Nat.succ_lt_succ_iff.mp hx₁
+
+/--
+For all natural numbers `m, n`, `m - n ∪ {m} ≈ m - n`.
+-/
+theorem diff_union_equinumerous_succ_diff {m n : ℕ} (hn: n ≤ m)
+  : Set.Iio m \ Set.Iio n ∪ {m} ≈ Set.Iio (Nat.succ m) \ Set.Iio n := by
+  refine ⟨fun x => x, ?_, ?_, ?_⟩
+  · intro x hx
+    simp at hx ⊢
+    apply Or.elim hx
+    · intro hx₁
+      rw [hx₁]
+      exact ⟨hn, by simp⟩
+    · intro ⟨hx₁, hx₂⟩
+      exact ⟨hx₁, calc x
+        _ < m := hx₂
+        _ < m + 1 := by simp⟩
+  · intro _ _ _ _ h
+    exact h
+  · unfold Set.SurjOn Set.image
+    rw [Set.subset_def]
+    simp only [
+      Set.Iio_diff_Iio,
+      gt_iff_lt,
+      not_lt,
+      ge_iff_le,
+      Set.mem_Ico,
+      Set.union_singleton,
+      lt_self_iff_false,
+      and_false,
+      Set.mem_insert_iff,
+      exists_eq_right,
+      Set.mem_setOf_eq,
+      and_imp
+    ]
+    intro x hn hm
+    apply Or.elim (Nat.lt_or_eq_of_lt hm)
+    · intro hx
+      right
+      exact ⟨hn, hx⟩
+    · intro hx
+      left
+      exact hx
+
+end Set

Common/Set/Function.lean

@@ -0,0 +1,235 @@
+import Mathlib.Data.Set.Function
+
+/-! # Common.Set.Function
+
+Additional theorems around functions defined on sets.
+-/
+
+namespace Set.Function
+
+/--
+Produce a new function that swaps the outputs of the two specified inputs.
+-/
+def swap [DecidableEq α] (f : α → β) (x₁ x₂ : α) (x : α) : β :=
+  if x = x₁ then f x₂ else
+  if x = x₂ then f x₁ else
+                 f x
+
+/--
+Swapping the same input yields the original function.
+-/
+@[simp]
+theorem swap_eq_eq_self [DecidableEq α] {f : α → β} {x : α}
+  : swap f x x = f := by
+  refine funext ?_
+  intro y
+  unfold swap
+  by_cases hy : y = x
+  · rw [if_pos hy, hy]
+  · rw [if_neg hy, if_neg hy]
+
+/--
+Swapping a function twice yields the original function.
+-/
+@[simp]
+theorem swap_swap_eq_self [DecidableEq α] {f : α → β} {x₁ x₂ : α}
+  : swap (swap f x₁ x₂) x₁ x₂ = f := by
+  refine funext ?_
+  intro y
+  by_cases hc₁ : x₂ = x₁
+  · rw [hc₁]
+    simp
+  rw [← Ne.def] at hc₁
+  unfold swap
+  by_cases hc₂ : y = x₁ <;>
+  by_cases hc₃ : y = x₂
+  · rw [if_pos hc₂, if_neg hc₁, if_pos rfl, ← hc₂]
+  · rw [if_pos hc₂, if_neg hc₁, if_pos rfl, ← hc₂]
+  · rw [if_neg hc₂, if_pos hc₃, if_pos rfl, ← hc₃]
+  · rw [if_neg hc₂, if_neg hc₃, if_neg hc₂, if_neg hc₃]
+
+/--
+If `f : A → B`, then a swapped variant of `f` also maps `A` into `B`.
+-/
+theorem swap_MapsTo_self [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : MapsTo f A B)
+  : MapsTo (swap f a₁ a₂) A B := by
+  intro x hx
+  unfold swap
+  by_cases hc₁ : x = a₁ <;> by_cases hc₂ : x = a₂
+  · rw [if_pos hc₁]
+    exact hf ha₂
+  · rw [if_pos hc₁]
+    exact hf ha₂
+  · rw [if_neg hc₁, if_pos hc₂]
+    exact hf ha₁
+  · rw [if_neg hc₁, if_neg hc₂]
+    exact hf hx
+
+/--
+The converse of `swap_MapsTo_self`.
+-/
+theorem self_MapsTo_swap [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : MapsTo (swap f a₁ a₂) A B)
+  : MapsTo f A B := by
+  rw [← @swap_swap_eq_self _ _ _ f a₁ a₂]
+  exact swap_MapsTo_self ha₁ ha₂ hf
+
+/--
+If `f : A → B`, then `f` maps `A` into `B` **iff** a swap of `f` maps `A` into
+`B`.
+-/
+theorem self_iff_swap_MapsTo [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A)
+  : MapsTo (swap f a₁ a₂) A B ↔ MapsTo f A B :=
+  ⟨self_MapsTo_swap ha₁ ha₂, swap_MapsTo_self ha₁ ha₂⟩
+
+/--
+If `f : A → B` is one-to-one, then a swapped variant of `f` is also one-to-one.
+-/
+theorem swap_InjOn_self [DecidableEq α]
+  {A : Set α} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : InjOn f A)
+  : InjOn (swap f a₁ a₂) A := by
+  intro x₁ hx₁ x₂ hx₂ h
+  unfold swap at h
+  by_cases hc₁ : x₁ = a₁ <;>
+  by_cases hc₂ : x₁ = a₂ <;>
+  by_cases hc₃ : x₂ = a₁ <;>
+  by_cases hc₄ : x₂ = a₂
+  · rw [hc₁, hc₃]
+  · rw [hc₁, hc₃]
+  · rw [hc₂, hc₄]
+  · rw [if_pos hc₁, if_neg hc₃, if_neg hc₄, ← hc₂] at h
+    exact hf hx₁ hx₂ h
+  · rw [hc₁, hc₃]
+  · rw [hc₁, hc₃]
+  · rw [if_pos hc₁, if_neg hc₃, if_pos hc₄, ← hc₁, ← hc₄] at h
+    exact hf hx₁ hx₂ h.symm
+  · rw [if_pos hc₁, if_neg hc₃, if_neg hc₄] at h
+    exact absurd (hf hx₂ ha₂ h.symm) hc₄
+  · rw [hc₂, hc₄]
+  · rw [if_neg hc₁, if_pos hc₂, if_pos hc₃, ← hc₂, ← hc₃] at h
+    exact hf hx₁ hx₂ h.symm
+  · rw [hc₂, hc₄]
+  · rw [if_neg hc₁, if_pos hc₂, if_neg hc₃, if_neg hc₄] at h
+    exact absurd (hf hx₂ ha₁ h.symm) hc₃
+  · rw [if_neg hc₁, if_neg hc₂, if_pos hc₃, ← hc₄] at h
+    exact hf hx₁ hx₂ h
+  · rw [if_neg hc₁, if_neg hc₂, if_pos hc₃] at h
+    exact absurd (hf hx₁ ha₂ h) hc₂
+  · rw [if_neg hc₁, if_neg hc₂, if_neg hc₃, if_pos hc₄] at h
+    exact absurd (hf hx₁ ha₁ h) hc₁
+  · rw [if_neg hc₁, if_neg hc₂, if_neg hc₃, if_neg hc₄] at h
+    exact hf hx₁ hx₂ h
+
+/--
+The converse of `swap_InjOn_self`.
+-/
+theorem self_InjOn_swap [DecidableEq α]
+  {A : Set α} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : InjOn (swap f a₁ a₂) A)
+  : InjOn f A := by
+  rw [← @swap_swap_eq_self _ _ _ f a₁ a₂]
+  exact swap_InjOn_self ha₁ ha₂ hf
+
+/--
+If `f : A → B`, then `f` is one-to-one **iff** a swap of `f` is one-to-one.
+-/
+theorem self_iff_swap_InjOn [DecidableEq α]
+  {A : Set α} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A)
+  : InjOn (swap f a₁ a₂) A ↔ InjOn f A :=
+  ⟨self_InjOn_swap ha₁ ha₂, swap_InjOn_self ha₁ ha₂⟩
+
+/--
+If `f : A → B` is onto, then a swapped variant of `f` is also onto.
+-/
+theorem swap_SurjOn_self [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : SurjOn f A B)
+  : SurjOn (swap f a₁ a₂) A B := by
+  show ∀ x, x ∈ B → ∃ a ∈ A, swap f a₁ a₂ a = x
+  intro x hx
+  have ⟨a, ha⟩ := hf hx
+  by_cases hc₁ : a = a₁
+  · refine ⟨a₂, ha₂, ?_⟩
+    unfold swap
+    by_cases hc₂ : a₁ = a₂
+    · rw [if_pos hc₂.symm, ← hc₂, ← hc₁]
+      exact ha.right
+    · rw [← Ne.def] at hc₂
+      rw [if_neg hc₂.symm, if_pos rfl, ← hc₁]
+      exact ha.right
+  · by_cases hc₂ : a = a₂
+    · unfold swap
+      refine ⟨a₁, ha₁, ?_⟩
+      rw [if_pos rfl, ← hc₂]
+      exact ha.right
+    · refine ⟨a, ha.left, ?_⟩
+      unfold swap
+      rw [if_neg hc₁, if_neg hc₂]
+      exact ha.right
+
+/--
+The converse of `swap_SurjOn_self`.
+-/
+theorem self_SurjOn_swap [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : SurjOn (swap f a₁ a₂) A B)
+  : SurjOn f A B := by
+  rw [← @swap_swap_eq_self _ _ _ f a₁ a₂]
+  exact swap_SurjOn_self ha₁ ha₂ hf
+
+/--
+If `f : A → B`, then `f` is onto **iff** a swap of `f` is onto.
+-/
+theorem self_iff_swap_SurjOn [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A)
+  : SurjOn (swap f a₁ a₂) A B ↔ SurjOn f A B :=
+  ⟨self_SurjOn_swap ha₁ ha₂, swap_SurjOn_self ha₁ ha₂⟩
+
+/--
+If `f : A → B` is a one-to-one correspondence, then a swapped variant of `f` is
+also a one-to-one correspondence.
+-/
+theorem swap_BijOn_self [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : BijOn f A B)
+  : BijOn (swap f a₁ a₂) A B := by
+  have ⟨hf₁, hf₂, hf₃⟩ := hf
+  exact ⟨
+    swap_MapsTo_self ha₁ ha₂ hf₁,
+    swap_InjOn_self ha₁ ha₂ hf₂,
+    swap_SurjOn_self ha₁ ha₂ hf₃
+  ⟩
+
+/--
+The converse of `swap_BijOn_self`.
+-/
+theorem self_BijOn_swap [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A) (hf : BijOn (swap f a₁ a₂) A B)
+  : BijOn f A B := by
+  have ⟨hf₁, hf₂, hf₃⟩ := hf
+  exact ⟨
+    self_MapsTo_swap ha₁ ha₂ hf₁,
+    self_InjOn_swap ha₁ ha₂ hf₂,
+    self_SurjOn_swap ha₁ ha₂ hf₃
+  ⟩
+
+/--
+If `f : A → B`, `f` is a one-to-one correspondence **iff** a swap of `f` is a
+one-to-one correspondence.
+-/
+theorem self_iff_swap_BijOn [DecidableEq α]
+  {A : Set α} {B : Set β} {f : α → β}
+  (ha₁ : a₁ ∈ A) (ha₂ : a₂ ∈ A)
+  : BijOn (swap f a₁ a₂) A B ↔ BijOn f A B :=
+  ⟨self_BijOn_swap ha₁ ha₂, swap_BijOn_self ha₁ ha₂⟩
+
+end Set.Function

Common/Set/Intervals.lean

@@ -1,4 +1,5 @@
 import Common.Logic.Basic
+import Mathlib.Data.Set.Function
 import Mathlib.Data.Set.Intervals.Basic
 
 namespace Set
@@ -8,6 +9,9 @@ namespace Set
 Additional theorems around intervals.
 -/
 
+/--
+If `m < n` then `{0, …, m - 1} ⊂ {0, …, n - 1}`.
+-/
 theorem Iio_nat_lt_ssubset {m n : ℕ} (h : m < n)
   : Iio m ⊂ Iio n := by
   rw [ssubset_def]
@@ -22,4 +26,22 @@ theorem Iio_nat_lt_ssubset {m n : ℕ} (h : m < n)
     simp only [not_forall, not_lt, exists_prop]
     exact ⟨m, h, by simp⟩
 
+/--
+It is never the case that the emptyset is surjective
+-/
+theorem SurjOn_emptyset_Iio_iff_eq_zero {n : ℕ} {f : α → ℕ}
+  : SurjOn f ∅ (Set.Iio n) ↔ n = 0 := by
+  apply Iff.intro
+  · intro h
+    unfold SurjOn at h
+    rw [subset_def] at h
+    simp only [mem_Iio, image_empty, mem_empty_iff_false] at h
+    by_contra nh
+    exact h 0 (Nat.pos_of_ne_zero nh)
+  · intro hn
+    unfold SurjOn
+    rw [hn, subset_def]
+    intro x hx
+    exact absurd hx (Nat.not_lt_zero x)
+
 end Set

DocGen4.lean

@@ -1,9 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.Process
-import DocGen4.Load
-import DocGen4.Output
-import DocGen4.LeanInk

DocGen4/LeanInk.lean

@@ -1,7 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.LeanInk.Process
-import DocGen4.LeanInk.Output

DocGen4/LeanInk/Output.lean

@@ -1,215 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving, Xubai Wang
--/
-import DocGen4.Output.Base
-import DocGen4.Output.ToHtmlFormat
-import Lean.Data.Json
-import LeanInk.Annotation.Alectryon
-
-namespace LeanInk.Annotation.Alectryon
-
-open DocGen4 Output
-open scoped DocGen4.Jsx
-
-structure AlectryonContext where
-  counter : Nat
-
-abbrev AlectryonT := StateT AlectryonContext
-abbrev AlectryonM := AlectryonT HtmlM
-
-def getNextButtonLabel : AlectryonM String := do
-  let val ← get
-  let newCounter := val.counter + 1
-  set { val with counter := newCounter }
-  return s!"plain-lean4-lean-chk{val.counter}"
-
-def TypeInfo.toHtml (tyi : TypeInfo) : AlectryonM Html := do
-  pure
-    <div class="alectryon-type-info-wrapper">
-      <small class="alectryon-type-info">
-        <div class="alectryon-goals">
-          <blockquote class="alectryon-goal">
-            <div class="goal-hyps">
-              <span class="hyp-type">
-                <var>{tyi.name}</var>
-                <b>: </b>
-                <span>[← DocGen4.Output.infoFormatToHtml tyi.type.fst]</span>
-              </span>
-            </div>
-          </blockquote>
-        </div>
-      </small>
-    </div>
-
-def Token.processSemantic (t : Token) : Html :=
-  match t.semanticType with
-  | some "Name.Attribute" => <span class="na">{t.raw}</span>
-  | some "Name.Variable" => <span class="nv">{t.raw}</span>
-  | some "Keyword" => <span class="k">{t.raw}</span>
-  | _ => Html.text t.raw
-
-def Token.toHtml (t : Token) : AlectryonM Html := do
-  -- Right now t.link is always none from LeanInk, ignore it
-  -- TODO: render docstring
-  let mut parts := #[]
-  if let some tyi := t.typeinfo then
-    parts := parts.push <| ← tyi.toHtml
-
-  parts := parts.push t.processSemantic
-
-  pure
-    -- TODO: Show rest of token
-    <span class="alectryon-token">
-      [parts]
-    </span>
-
-def Contents.toHtml : Contents → AlectryonM Html
-  | .string value =>
-    pure
-      <span class="alectryon-wsp">
-        {value}
-      </span>
-  | .experimentalTokens values => do
-    let values ← values.mapM Token.toHtml
-    pure
-      <span class="alectryon-wsp">
-        [values]
-      </span>
-
-def Hypothesis.toHtml (h : Hypothesis) : AlectryonM Html := do
-  let mut hypParts := #[<var>[h.names.intersperse ", " |>.map Html.text |>.toArray]</var>]
-  if h.body.snd != "" then
-    hypParts := hypParts.push
-      <span class="hyp-body">
-        <b>:= </b>
-        <span>[← infoFormatToHtml h.body.fst]</span>
-      </span>
-  hypParts := hypParts.push
-      <span class="hyp-type">
-        <b>: </b>
-        <span >[← infoFormatToHtml h.type.fst]</span>
-      </span>
-
-  pure
-    <span>
-      [hypParts]
-    </span>
-
-def Goal.toHtml (g : Goal) : AlectryonM Html := do
-  let mut hypotheses := #[]
-  for hyp in g.hypotheses do
-    let rendered ← hyp.toHtml
-    hypotheses := hypotheses.push rendered
-    hypotheses := hypotheses.push <br/>
-  let conclusionHtml ←
-    match g.conclusion with
-    | .typed info _ => infoFormatToHtml info
-    | .untyped str => pure #[Html.text str]
-
-  pure
-    <blockquote class="alectryon-goal">
-      <div class="goal-hyps">
-        [hypotheses]
-      </div>
-      <span class="goal-separator">
-        <hr><span class="goal-name">{g.name}</span></hr>
-      </span>
-      <div class="goal-conclusion">
-        [conclusionHtml]
-      </div>
-    </blockquote>
-
-def Message.toHtml (m : Message) : AlectryonM Html := do
-  pure
-    <blockquote class="alectryon-message">
-      -- TODO: This might have to be done in a fancier way
-      {m.contents}
-    </blockquote>
-
-def Sentence.toHtml (s : Sentence) : AlectryonM Html := do
-  let messages :=
-    if s.messages.size > 0 then
-      #[
-        <div class="alectryon-messages">
-          [← s.messages.mapM Message.toHtml]
-        </div>
-      ]
-    else
-      #[]
-  
-  let goals :=
-    if s.goals.size > 0 then
-      -- TODO: Alectryon has a "alectryon-extra-goals" here, implement it
-      #[
-        <div class="alectryon-goals">
-          [← s.goals.mapM Goal.toHtml]
-        </div>
-      ]
-    else
-      #[]
-
-  let buttonLabel ← getNextButtonLabel
-
-  pure
-    <span class="alectryon-sentence">
-      <input class="alectryon-toggle" id={buttonLabel} style="display: none" type="checkbox"/>
-      <label class="alectryon-input" for={buttonLabel}>
-        {← s.contents.toHtml}
-      </label>
-      <small class="alectryon-output">
-        [messages]
-        [goals]
-      </small>
-    </span>
-
-def Text.toHtml (t : Text) : AlectryonM Html := t.contents.toHtml
-
-def Fragment.toHtml : Fragment → AlectryonM Html
-  | .text value => value.toHtml
-  | .sentence value => value.toHtml
-
-def baseHtml (content : Array Html) : AlectryonM Html := do
-  let banner :=
-    <div «class»="alectryon-banner">
-      Built with <a href="https://github.com/leanprover/doc-gen4">doc-gen4</a>, running Lean4.
-      Bubbles (<span class="alectryon-bubble"></span>) indicate interactive fragments: hover for details, tap to reveal contents.
-      Use <kbd>Ctrl+↑</kbd> <kbd>Ctrl+↓</kbd> to navigate, <kbd>Ctrl+🖱️</kbd> to focus.
-      On Mac, use <kbd>Cmd</kbd> instead of <kbd>Ctrl</kbd>.
-    </div>
-
-  pure
-    <html lang="en" class="alectryon-standalone">
-      <head>
-        <meta charset="UTF-8"/>
-        <meta name="viewport" content="width=device-width, initial-scale=1"/>
-
-        <link rel="stylesheet" href={s!"{← getRoot}src/alectryon.css"}/>
-        <link rel="stylesheet" href={s!"{← getRoot}src/pygments.css"}/>
-        <link rel="stylesheet" href={s!"{← getRoot}src/docutils_basic.css"}/>
-        <link rel="shortcut icon" href={s!"{← getRoot}favicon.ico"}/>
-
-        <script defer="true" src={s!"{← getRoot}src/alectryon.js"}></script>
-      </head>
-      <body>
-        <article class="alectryon-root alectryon-centered">
-          {banner}
-          <pre class="alectryon-io highlight">
-            [content]
-          </pre>
-        </article>
-      </body>
-    </html>
-
-def annotationsToFragments (as : List Annotation.Annotation) : AnalysisM (List Fragment) := do
-  let config ← read
-  annotateFileWithCompounds [] config.inputFileContents as
-
--- TODO: rework monad mess
-def renderAnnotations (as : List Annotation.Annotation) : HtmlT AnalysisM Html := do
-  let fs ← annotationsToFragments as
-  let (html, _) ← fs.mapM Fragment.toHtml >>= (baseHtml ∘ List.toArray) |>.run { counter := 0 }
-  return html
-
-end LeanInk.Annotation.Alectryon

DocGen4/LeanInk/Process.lean

@@ -1,57 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-import LeanInk.Analysis
-import LeanInk.Annotation
-import DocGen4.LeanInk.Output
-import DocGen4.Output.Base
-
-namespace DocGen4.Process.LeanInk
-
-open Lean
-open DocGen4.Output
-
-def docGenOutput (as : List LeanInk.Annotation.Annotation) : HtmlT LeanInk.AnalysisM UInt32 := do
-  let some modName ← getCurrentName | unreachable!
-  let srcHtml ← LeanInk.Annotation.Alectryon.renderAnnotations as
-  let srcDir := moduleNameToDirectory srcBasePath modName
-  let srcPath := moduleNameToFile srcBasePath modName
-  IO.FS.createDirAll srcDir
-  IO.FS.writeFile srcPath srcHtml.toString
-  return 0
-
-def execAuxM : HtmlT LeanInk.AnalysisM UInt32 := do
-  let ctx ← readThe SiteContext
-  let baseCtx ← readThe SiteBaseContext
-  let outputFn := (docGenOutput · |>.run ctx baseCtx)
-  return ← LeanInk.Analysis.runAnalysis {
-    name := "doc-gen4"
-    genOutput := outputFn
-  }
-
-def execAux (config : LeanInk.Configuration) : HtmlT IO UInt32 := do
-  execAuxM.run (← readThe SiteContext) (← readThe SiteBaseContext) |>.run config
-
-@[implemented_by enableInitializersExecution]
-private def enableInitializersExecutionWrapper : IO Unit := return ()
-
-def runInk (sourceFilePath : System.FilePath) : HtmlT IO Unit := do
-  let contents ← IO.FS.readFile sourceFilePath
-  let config := {
-    inputFilePath := sourceFilePath
-    inputFileContents := contents
-    lakeFile := none
-    verbose := false
-    prettifyOutput := true
-    experimentalTypeInfo := true
-    experimentalDocString := true
-    experimentalSemanticType := true
-  }
-  enableInitializersExecutionWrapper
-  if (← execAux config) != 0 then
-    throw <| IO.userError s!"Analysis for \"{sourceFilePath}\" failed!"
-
-end DocGen4.Process.LeanInk

DocGen4/Load.lean

@@ -1,61 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-
-import Lean
-import Lake
-import Lake.CLI.Main
-import DocGen4.Process
-import Lean.Data.HashMap
-
-namespace DocGen4
-
-open Lean System IO
-/--
-Sets up a lake workspace for the current project. Furthermore initialize
-the Lean search path with the path to the proper compiler from lean-toolchain
-as well as all the dependencies.
--/
-def lakeSetup : IO (Except UInt32 Lake.Workspace) := do
-  let (leanInstall?, lakeInstall?) ← Lake.findInstall?
-  let config := Lake.mkLoadConfig.{0} {leanInstall?, lakeInstall?}
-  match ←(EIO.toIO' config) with
-  | .ok config =>
-    let ws : Lake.Workspace ← Lake.loadWorkspace config
-      |>.run Lake.MonadLog.eio
-      |>.toIO (λ _ => IO.userError "Failed to load Lake workspace")
-    pure <| Except.ok ws
-  | .error err =>
-    throw <| IO.userError err.toString
-
-def envOfImports (imports : List Name) : IO Environment := do
- importModules (imports.map (Import.mk · false)) Options.empty
-
-def loadInit (imports : List Name) : IO Hierarchy := do
- let env ← envOfImports imports
- pure <| Hierarchy.fromArray env.header.moduleNames
-
-/--
-Load a list of modules from the current Lean search path into an `Environment`
-to process for documentation.
--/
-def load (task : Process.AnalyzeTask) : IO (Process.AnalyzerResult × Hierarchy) := do
-  let env ← envOfImports task.getLoad
-  IO.println "Processing modules"
-  let config := {
-    -- TODO: parameterize maxHeartbeats
-    maxHeartbeats := 100000000,
-    options := ⟨[(`pp.tagAppFns, true)]⟩,
-    -- TODO: Figure out whether this could cause some bugs
-    fileName := default,
-    fileMap := default,
-  }
-
-  Prod.fst <$> Meta.MetaM.toIO (Process.process task) config { env := env } {} {}
-
-def loadCore : IO (Process.AnalyzerResult × Hierarchy) := do
-  load <| .loadAll [`Init, `Lean, `Lake]
-
-end DocGen4

DocGen4/Output.lean

@@ -1,156 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-import Lake
-import DocGen4.Process
-import DocGen4.Output.Base
-import DocGen4.Output.Index
-import DocGen4.Output.Module
-import DocGen4.Output.NotFound
-import DocGen4.Output.Find
-import DocGen4.Output.SourceLinker
-import DocGen4.Output.Search
-import DocGen4.Output.ToJson
-import DocGen4.Output.FoundationalTypes
-import DocGen4.LeanInk.Process
-import Lean.Data.HashMap
-
-namespace DocGen4
-
-open Lean IO System Output Process
-
-def htmlOutputSetup (config : SiteBaseContext) : IO Unit := do
-  let findBasePath := basePath / "find"
-
-  -- Base structure
-  FS.createDirAll basePath
-  FS.createDirAll findBasePath
-  FS.createDirAll srcBasePath
-  FS.createDirAll declarationsBasePath
-
-  -- All the doc-gen static stuff
-  let indexHtml := ReaderT.run index config |>.toString
-  let notFoundHtml := ReaderT.run notFound config |>.toString
-  let foundationalTypesHtml := ReaderT.run foundationalTypes config |>.toString
-  let navbarHtml := ReaderT.run navbar config |>.toString
-  let searchHtml := ReaderT.run search config |>.toString
-  let docGenStatic := #[
-    ("style.css", styleCss),
-    ("declaration-data.js", declarationDataCenterJs),
-    ("color-scheme.js", colorSchemeJs),
-    ("nav.js", navJs),
-    ("how-about.js", howAboutJs),
-    ("search.html", searchHtml),
-    ("search.js", searchJs),
-    ("mathjax-config.js", mathjaxConfigJs),
-    ("instances.js", instancesJs),
-    ("importedBy.js", importedByJs),
-    ("index.html", indexHtml),
-    ("foundational_types.html", foundationalTypesHtml),
-    ("404.html", notFoundHtml),
-    ("navbar.html", navbarHtml)
-  ]
-  for (fileName, content) in docGenStatic do
-    FS.writeFile (basePath / fileName) content
-
-  let findHtml := ReaderT.run find { config with depthToRoot := 1 } |>.toString
-  let findStatic := #[
-    ("index.html", findHtml),
-    ("find.js", findJs)
-  ]
-  for (fileName, content) in findStatic do
-    FS.writeFile (findBasePath / fileName) content
-
-  let alectryonStatic := #[
-    ("alectryon.css", alectryonCss),
-    ("alectryon.js", alectryonJs),
-    ("docutils_basic.css", docUtilsCss),
-    ("pygments.css", pygmentsCss)
-  ]
-
-  for (fileName, content) in alectryonStatic do
-    FS.writeFile (srcBasePath / fileName) content
-
-def htmlOutputDeclarationDatas (result : AnalyzerResult) : HtmlT IO Unit := do
-  for (_, mod) in result.moduleInfo.toArray do
-    let jsonDecls ← Module.toJson mod
-    FS.writeFile (declarationsBasePath / s!"declaration-data-{mod.name}.bmp") (toJson jsonDecls).compress
-
-def htmlOutputResults (baseConfig : SiteBaseContext) (result : AnalyzerResult) (ws : Lake.Workspace) (ink : Bool) : IO Unit := do
-  let config : SiteContext := {
-    result := result,
-    sourceLinker := ← SourceLinker.sourceLinker ws
-    leanInkEnabled := ink
-  }
-
-  FS.createDirAll basePath
-  FS.createDirAll declarationsBasePath
-
-  -- Rendering the entire lean compiler takes time....
-  --let sourceSearchPath := ((←Lean.findSysroot) / "src" / "lean") :: ws.root.srcDir :: ws.leanSrcPath
-  let sourceSearchPath := ws.root.srcDir :: ws.leanSrcPath
-
-  discard <| htmlOutputDeclarationDatas result |>.run config baseConfig
-
-  for (modName, module) in result.moduleInfo.toArray do
-    let fileDir := moduleNameToDirectory basePath modName
-    let filePath := moduleNameToFile basePath modName
-    -- path: 'basePath/module/components/till/last.html'
-    -- The last component is the file name, so we drop it from the depth to root.
-    let baseConfig := { baseConfig with
-      depthToRoot := modName.components.dropLast.length
-      currentName := some modName
-    }
-    let moduleHtml := moduleToHtml module |>.run config baseConfig
-    FS.createDirAll fileDir
-    FS.writeFile filePath moduleHtml.toString
-    if ink then
-      if let some inputPath ← Lean.SearchPath.findModuleWithExt sourceSearchPath "lean" module.name then
-        IO.println s!"Inking: {modName.toString}"
-        -- path: 'basePath/src/module/components/till/last.html'
-        -- The last component is the file name, however we are in src/ here so dont drop it this time
-        let baseConfig := {baseConfig with depthToRoot := modName.components.length }
-        Process.LeanInk.runInk inputPath |>.run config baseConfig
-
-def getSimpleBaseContext (hierarchy : Hierarchy) : IO SiteBaseContext := do
-  return {
-    depthToRoot := 0,
-    currentName := none,
-    hierarchy
-    projectGithubUrl := ← SourceLinker.getProjectGithubUrl
-    projectCommit := ← SourceLinker.getProjectCommit
-  }
-
-def htmlOutputIndex (baseConfig : SiteBaseContext) : IO Unit := do
-  htmlOutputSetup baseConfig
-
-  let mut index : JsonIndex := {}
-  let mut headerIndex : JsonHeaderIndex := {}
-  for entry in ← System.FilePath.readDir declarationsBasePath do
-    if entry.fileName.startsWith "declaration-data-" && entry.fileName.endsWith ".bmp" then
-      let fileContent ← FS.readFile entry.path
-      let .ok jsonContent := Json.parse fileContent | unreachable!
-      let .ok (module : JsonModule) := fromJson? jsonContent | unreachable!
-      index := index.addModule module |>.run baseConfig
-      headerIndex := headerIndex.addModule module
-
-  let finalJson := toJson index
-  let finalHeaderJson := toJson headerIndex
-  -- The root JSON for find
-  FS.writeFile (declarationsBasePath / "declaration-data.bmp") finalJson.compress
-  FS.writeFile (declarationsBasePath / "header-data.bmp") finalHeaderJson.compress
-
-/--
-The main entrypoint for outputting the documentation HTML based on an
-`AnalyzerResult`.
--/
-def htmlOutput (result : AnalyzerResult) (hierarchy : Hierarchy) (ws : Lake.Workspace) (ink : Bool) : IO Unit := do
-  let baseConfig ← getSimpleBaseContext hierarchy
-  htmlOutputResults baseConfig result ws ink
-  htmlOutputIndex baseConfig
-
-end DocGen4
-

DocGen4/Output/Base.lean

@@ -1,285 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.Process
-import DocGen4.Output.ToHtmlFormat
-
-namespace DocGen4.Output
-
-open scoped DocGen4.Jsx
-open Lean System Widget Elab Process
-
-def basePath := FilePath.mk "." / "build" / "doc"
-def srcBasePath := basePath / "src"
-def declarationsBasePath := basePath / "declarations"
-
-/--
-The context used in the `BaseHtmlM` monad for HTML templating.
--/
-structure SiteBaseContext where
-
-  /--
-  The module hierarchy as a tree structure.
-  -/
-  hierarchy : Hierarchy
-  /--
-  How far away we are from the page root, used for relative links to the root.
-  -/
-  depthToRoot: Nat
-  /--
-  The name of the current module if there is one, there exist a few
-  pages that don't have a module name.
-  -/
-  currentName : Option Name
-  /--
-  The Github URL of the project that we are building docs for.
-  -/
-  projectGithubUrl : String
-  /--
-  The commit of the project that we are building docs for.
-  -/
-  projectCommit : String
-
-/--
-The context used in the `HtmlM` monad for HTML templating.
--/
-structure SiteContext where
-  /--
-  The full analysis result from the Process module.
-  -/
-  result : AnalyzerResult
-  /--
-  A function to link declaration names to their source URLs, usually Github ones.
-  -/
-  sourceLinker : Name → Option DeclarationRange → String
-  /--
-  Whether LeanInk is enabled
-  -/
-  leanInkEnabled : Bool
-
-def setCurrentName (name : Name) (ctx : SiteBaseContext) := {ctx with currentName := some name}
-
-abbrev BaseHtmlT := ReaderT SiteBaseContext
-abbrev BaseHtmlM := BaseHtmlT Id
-
-abbrev HtmlT (m) := ReaderT SiteContext (BaseHtmlT m)
-abbrev HtmlM := HtmlT Id
-
-def HtmlT.run (x : HtmlT m α) (ctx : SiteContext) (baseCtx : SiteBaseContext) : m α :=
-  ReaderT.run x ctx |>.run baseCtx
-
-def HtmlM.run (x : HtmlM α) (ctx : SiteContext) (baseCtx : SiteBaseContext) : α :=
-  ReaderT.run x ctx |>.run baseCtx |>.run
-
-instance [Monad m] : MonadLift HtmlM (HtmlT m) where
-  monadLift x := do return x.run (← readThe SiteContext) (← readThe SiteBaseContext)
-
-instance [Monad m] : MonadLift BaseHtmlM (BaseHtmlT m) where
-  monadLift x := do return x.run (← readThe SiteBaseContext)
-
-/--
-Obtains the root URL as a relative one to the current depth.
--/
-def getRoot : BaseHtmlM String := do
-  let rec go: Nat -> String
-  | 0 => "./"
-  | Nat.succ n' => "../" ++ go n'
-  let d <- SiteBaseContext.depthToRoot <$> read
-  return (go d)
-
-def getHierarchy : BaseHtmlM Hierarchy := do return (← read).hierarchy
-def getCurrentName : BaseHtmlM (Option Name) := do return (← read).currentName
-def getResult : HtmlM AnalyzerResult := do return (← read).result
-def getSourceUrl (module : Name) (range : Option DeclarationRange): HtmlM String := do return (← read).sourceLinker module range
-def leanInkEnabled? : HtmlM Bool := do return (← read).leanInkEnabled
-def getProjectGithubUrl : BaseHtmlM String := do return (← read).projectGithubUrl
-def getProjectCommit : BaseHtmlM String := do return (← read).projectCommit
-
-/--
-If a template is meant to be extended because it for example only provides the
-header but no real content this is the way to fill the template with content.
-This is untyped so HtmlM and BaseHtmlM can be mixed.
--/
-def templateExtends {α β} {m} [Bind m] (base : α → m β) (new : m α) : m β :=
-  new >>= base
-
-def templateLiftExtends {α β} {m n} [Bind m] [MonadLift n m] (base : α → n β) (new : m α) : m β :=
-  new >>= (monadLift ∘ base)
-
-/-
-Returns the doc-gen4 link to a module `NameExt`.
--/
-def moduleNameExtToLink (n : NameExt) : BaseHtmlM String := do
-  let parts := n.name.components.map Name.toString
-  return (← getRoot) ++ (parts.intersperse "/").foldl (· ++ ·) "" ++ "." ++ n.ext.toString
-
-/--
-Returns the doc-gen4 link to a module name.
--/
-def moduleNameToHtmlLink (n : Name) : BaseHtmlM String :=
-  moduleNameExtToLink ⟨n, .html⟩
-
-/--
-Returns the HTML doc-gen4 link to a module name.
--/
-def moduleToHtmlLink (module : Name) : BaseHtmlM Html := do
-  return <a href={← moduleNameToHtmlLink module}>{module.toString}</a>
-
-/--
-Returns the LeanInk link to a module name.
--/
-def moduleNameToInkLink (n : Name) : BaseHtmlM String := do
-  let parts := "src" :: n.components.map Name.toString
-  return (← getRoot) ++ (parts.intersperse "/").foldl (· ++ ·) "" ++ ".html"
-
-/--
-Returns the path to the HTML file that contains information about a module.
--/
-def moduleNameToFile (basePath : FilePath) (n : Name) : FilePath :=
-  let parts := n.components.map Name.toString
-  FilePath.withExtension (basePath / parts.foldl (· / ·) (FilePath.mk ".")) "html"
-
-/--
-Returns the directory of the HTML file that contains information about a module.
--/
-def moduleNameToDirectory (basePath : FilePath) (n : Name) : FilePath :=
-  let parts := n.components.dropLast.map Name.toString
-  basePath / parts.foldl (· / ·) (FilePath.mk ".")
-
-section Static
-/-!
-The following section contains all the statically included files that
-are used in documentation generation, notably JS and CSS ones.
--/
-  def styleCss : String := include_str "../../static/style.css"
-  def declarationDataCenterJs : String := include_str "../../static/declaration-data.js"
-  def colorSchemeJs : String := include_str "../../static/color-scheme.js"
-  def navJs : String := include_str "../../static/nav.js"
-  def howAboutJs : String := include_str "../../static/how-about.js"
-  def searchJs : String := include_str "../../static/search.js"
-  def instancesJs : String := include_str "../../static/instances.js"
-  def importedByJs : String := include_str "../../static/importedBy.js"
-  def findJs : String := include_str "../../static/find/find.js"
-  def mathjaxConfigJs : String := include_str "../../static/mathjax-config.js"
-
-  def alectryonCss : String := include_str "../../static/alectryon/alectryon.css"
-  def alectryonJs : String := include_str "../../static/alectryon/alectryon.js"
-  def docUtilsCss : String  := include_str "../../static/alectryon/docutils_basic.css"
-  def pygmentsCss : String  := include_str "../../static/alectryon/pygments.css"
-end Static
-
-/--
-Returns the doc-gen4 link to a declaration name.
--/
-def declNameToLink (name : Name) : HtmlM String := do
-  let res ← getResult
-  let module := res.moduleNames[res.name2ModIdx.find! name |>.toNat]!
-  return (← moduleNameToHtmlLink module) ++ "#" ++ name.toString
-
-/--
-Returns the HTML doc-gen4 link to a declaration name.
--/
-def declNameToHtmlLink (name : Name) : HtmlM Html := do
-  return <a href={← declNameToLink name}>{name.toString}</a>
-
-/--
-Returns the LeanInk link to a declaration name.
--/
-def declNameToInkLink (name : Name) : HtmlM String := do
-  let res ← getResult
-  let module := res.moduleNames[res.name2ModIdx.find! name |>.toNat]!
-  return (← moduleNameToInkLink module) ++ "#" ++ name.toString
-
-/--
-Returns a name splitted into parts.
-Together with "break_within" CSS class this helps browser to break a name
-nicely.
--/
-def breakWithin (name: String) : (Array Html) :=
-  name.splitOn "."
-    |> .map (fun (s: String) => <span class="name">{s}</span>)
-    |> .intersperse "."
-    |> List.toArray
-
-/--
-Returns the HTML doc-gen4 link to a declaration name with "break_within"
-set as class.
--/
-def declNameToHtmlBreakWithinLink (name : Name) : HtmlM Html := do
-  return <a class="break_within" href={← declNameToLink name}>
-      [breakWithin name.toString]
-    </a>
-
-/--
-In Lean syntax declarations the following pattern is quite common:
-```
-syntax term " + " term : term
-```
-that is, we place spaces around the operator in the middle. When the
-`InfoTree` framework provides us with information about what source token
-corresponds to which identifier it will thus say that `" + "` corresponds to
-`HAdd.hadd`. This is however not the way we want this to be linked, in the HTML
-only `+` should be linked, taking care of this is what this function is
-responsible for.
--/
-def splitWhitespaces (s : String) : (String × String × String) := Id.run do
-  let front := "".pushn ' ' <| s.offsetOfPos (s.find (!Char.isWhitespace ·))
-  let mut s := s.trimLeft
-  let back := "".pushn ' ' (s.length - s.offsetOfPos (s.find Char.isWhitespace))
-  s := s.trimRight
-  (front, s, back)
-
-/--
-Turns a `CodeWithInfos` object, that is basically a Lean syntax tree with
-information about what the identifiers mean, into an HTML object that links
-to as much information as possible.
--/
-partial def infoFormatToHtml (i : CodeWithInfos) : HtmlM (Array Html) := do
-  match i with
-  | .text t => return #[Html.escape t]
-  | .append tt => tt.foldlM (fun acc t => do return acc ++ (← infoFormatToHtml t)) #[]
-  | .tag a t =>
-    match a.info.val.info with
-    | Info.ofTermInfo i =>
-      let cleanExpr :=  i.expr.consumeMData
-      match cleanExpr with
-      | .const name _ =>
-        -- TODO: this is some very primitive blacklisting but real Blacklisting needs MetaM
-        -- find a better solution
-        if (← getResult).name2ModIdx.contains name then
-          match t with
-          | .text t =>
-            let (front, t, back) := splitWhitespaces <| Html.escape t
-            let elem := <a href={← declNameToLink name}>{t}</a>
-            return #[Html.text front, elem, Html.text back]
-          | _ =>
-            return #[<a href={← declNameToLink name}>[← infoFormatToHtml t]</a>]
-        else
-         return #[<span class="fn">[← infoFormatToHtml t]</span>]
-      | .sort _ =>
-        match t with
-        | .text t =>
-          let mut sortPrefix :: rest := t.splitOn " " | unreachable!
-          let sortLink := <a href={s!"{← getRoot}foundational_types.html"}>{sortPrefix}</a>
-          if rest != [] then
-            rest := " " :: rest
-          return #[sortLink, Html.text <| String.join rest]
-        | _ =>
-          return #[<a href={s!"{← getRoot}foundational_types.html"}>[← infoFormatToHtml t]</a>]
-      | _ =>
-         return #[<span class="fn">[← infoFormatToHtml t]</span>]
-    | _ => return #[<span class="fn">[← infoFormatToHtml t]</span>]
-
-def baseHtmlHeadDeclarations : BaseHtmlM (Array Html) := do
-  return #[
-    <meta charset="UTF-8"/>,
-    <meta name="viewport" content="width=device-width, initial-scale=1"/>,
-    <link rel="stylesheet" href={s!"{← getRoot}style.css"}/>,
-    <link rel="stylesheet" href={s!"{← getRoot}src/pygments.css"}/>,
-    <link rel="shortcut icon" href={s!"{← getRoot}favicon.ico"}/>,
-    <link rel="prefetch" href={s!"{← getRoot}/declarations/declaration-data.bmp"} as="image"/>
-  ]
-
-end DocGen4.Output

DocGen4/Output/Class.lean

@@ -1,22 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.Structure
-import DocGen4.Process
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-open Lean
-
-def classInstancesToHtml (className : Name) : HtmlM Html := do
-  pure
-    <details «class»="instances">
-        <summary>Instances</summary>
-        <ul id={s!"instances-list-{className}"} class="instances-list"></ul>
-    </details>
-
-def classToHtml (i : Process.ClassInfo) : HtmlM (Array Html) := do
-  structureToHtml i
-
-end Output
-end DocGen4

DocGen4/Output/ClassInductive.lean

@@ -1,14 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.Class
-import DocGen4.Output.Inductive
-import DocGen4.Process
-
-
-namespace DocGen4
-namespace Output
-
-def classInductiveToHtml (i : Process.ClassInductiveInfo) : HtmlM (Array Html) := do
-  inductiveToHtml i
-
-end Output
-end DocGen4

DocGen4/Output/Definition.lean

@@ -1,51 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.DocString
-import DocGen4.Process
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-open Lean Widget
-
-/-- This is basically an arbitrary number that seems to work okay. -/
-def equationLimit : Nat := 200
-
-def equationToHtml (c : CodeWithInfos) : HtmlM Html := do
-  return <li class="equation">[← infoFormatToHtml c]</li>
-
-/--
-Attempt to render all `simp` equations for this definition. At a size
-defined in `equationLimit` we stop trying since they:
-- are too ugly to read most of the time
-- take too long
--/
-def equationsToHtml (i : Process.DefinitionInfo) : HtmlM (Array Html) := do
-  if let some eqs := i.equations then
-    let equationsHtml ← eqs.mapM equationToHtml
-    let filteredEquationsHtml := equationsHtml.filter (·.textLength < equationLimit)
-    if equationsHtml.size ≠ filteredEquationsHtml.size then
-      return #[
-        <details>
-          <summary>Equations</summary>
-          <ul class="equations">
-            <li class="equation">One or more equations did not get rendered due to their size.</li>
-            [filteredEquationsHtml]
-          </ul>
-        </details>
-      ]
-    else
-      return #[
-        <details>
-          <summary>Equations</summary>
-          <ul class="equations">
-            [filteredEquationsHtml]
-          </ul>
-        </details>
-      ]
-  else
-    return #[]
-
-end Output
-end DocGen4
-

DocGen4/Output/DocString.lean

@@ -1,216 +0,0 @@
-import CMark
-import DocGen4.Output.Template
-import Lean.Data.Parsec
-import UnicodeBasic
-
-open Lean Xml Parser Parsec DocGen4.Process
-
-namespace DocGen4
-namespace Output
-
-/-- Auxiliary function for `splitAround`. -/
-@[specialize] partial def splitAroundAux (s : String) (p : Char → Bool) (b i : String.Pos) (r : List String) : List String :=
-  if s.atEnd i then
-    let r := (s.extract b i)::r
-    r.reverse
-  else
-    let c := s.get i
-    if p c then
-      let i := s.next i
-      splitAroundAux s p i i (c.toString::s.extract b (i-⟨1⟩)::r)
-    else
-      splitAroundAux s p b (s.next i) r
-
-/--
-  Similar to `Stirng.split` in Lean core, but keeps the separater.
-  e.g. `splitAround "a,b,c" (fun c => c = ',') = ["a", ",", "b", ",", "c"]`
--/
-def splitAround (s : String) (p : Char → Bool) : List String := splitAroundAux s p 0 0 []
-
-instance : Inhabited Element := ⟨"", Lean.RBMap.empty, #[]⟩
-
-/-- Parse an array of Xml/Html document from String. -/
-def manyDocument : Parsec (Array Element) := many (prolog *> element <* many Misc) <* eof
-
-/--
-  Generate id for heading elements, with the following rules:
-
-  1. Characters in `letter`, `mark`, `number` and `symbol` unicode categories are preserved.
-  2. Any sequences of Characters in `punctuation`, `separator` and `other` categories are replaced by a single dash.
-  3. Cases (upper and lower) are preserved.
-  4. Xml/Html tags are ignored.
--/
-partial def xmlGetHeadingId (el : Xml.Element) : String :=
-  elementToPlainText el |> replaceCharSeq unicodeToDrop "-"
-  where
-    elementToPlainText el := match el with
-    | (Element.Element _ _ contents) =>
-      "".intercalate (contents.toList.map contentToPlainText)
-    contentToPlainText c := match c with
-    | Content.Element el => elementToPlainText el
-    | Content.Comment _ => ""
-    | Content.Character s => s
-    replaceCharSeq pattern replacement s :=
-      s.split pattern
-      |>.filter (!·.isEmpty)
-      |> replacement.intercalate
-    unicodeToDrop (c : Char) : Bool :=
-      let cats := [
-        Unicode.GeneralCategory.P, -- punctuation
-        Unicode.GeneralCategory.Z, -- separator
-        Unicode.GeneralCategory.C -- other
-      ]
-      cats.any (Unicode.isInGeneralCategory c)
-
-/--
-  This function try to find the given name, both globally and in current module.
-
-  For global search, a precise name is need. If the global search fails, the function
-  tries to find a local one that ends with the given search name.
--/
-def nameToLink? (s : String) : HtmlM (Option String) := do
-  let res ← getResult
-  if let some name := Lean.Syntax.decodeNameLit ("`" ++ s) then
-    -- with exactly the same name
-    if res.name2ModIdx.contains name then
-      declNameToLink name
-    -- module name
-    else if res.moduleNames.contains name then
-      moduleNameToHtmlLink name
-    -- find similar name in the same module
-    else
-      match (← getCurrentName) with
-      | some currentName =>
-        match res.moduleInfo.find! currentName |>.members |> filterDocInfo |>.find? (sameEnd ·.getName name) with
-        | some info =>
-          declNameToLink info.getName
-        | _ => return none
-      | _ => return none
-  else
-    return none
-  where
-    -- check if two names have the same ending components
-    sameEnd n1 n2 :=
-      List.zip n1.componentsRev n2.componentsRev
-      |>.all fun ⟨a, b⟩ => a == b
-
-/--
-  Extend links with following rules:
-
-  1. if the link starts with `##`, a name search is used and will panic if not found
-  2. if the link starts with `#`, it's treated as id link, no modification
-  3. if the link starts with `http`, it's an absolute one, no modification
-  4. otherwise it's a relative link, extend it with base url
--/
-def extendLink (s : String)  : HtmlM String := do
-  -- for intra doc links
-  if s.startsWith "##" then
-    if let some link ← nameToLink? (s.drop 2) then
-      return link
-    else
-      panic! s!"Cannot find {s.drop 2}, only full name and abbrev in current module is supported"
-  -- for id
-  else if s.startsWith "#" then
-    return s
-  -- for absolute and relative urls
-  else if s.startsWith "http" then
-    return s
-  else return ((← getRoot) ++ s)
-
-/-- Add attributes for heading. -/
-def addHeadingAttributes (el : Element) (modifyElement : Element → HtmlM Element) : HtmlM Element := do
-  match el with
-  | Element.Element name attrs contents => do
-    let id := xmlGetHeadingId el
-    let anchorAttributes := Lean.RBMap.empty
-      |>.insert "class" "hover-link"
-      |>.insert "href" s!"#{id}"
-    let anchor := Element.Element "a" anchorAttributes #[Content.Character "#"]
-    let newAttrs := attrs
-      |>.insert "id" id
-      |>.insert "class" "markdown-heading"
-    let newContents := (←
-      contents.mapM (fun c => match c with
-      | Content.Element e => return Content.Element (← modifyElement e)
-      | _ => pure c))
-      |>.push (Content.Character " ")
-      |>.push (Content.Element anchor)
-    return ⟨ name, newAttrs, newContents⟩
-
-/-- Extend anchor links. -/
-def extendAnchor (el : Element) : HtmlM Element := do
-  match el with
-  | Element.Element name attrs contents =>
-    let newAttrs ← match attrs.find? "href" with
-    | some href => pure (attrs.insert "href" (← extendLink href))
-    | none => pure attrs
-    return ⟨ name, newAttrs, contents⟩
-
-/-- Automatically add intra documentation link for inline code span. -/
-def autoLink (el : Element) : HtmlM Element := do
-  match el with
-  | Element.Element name attrs contents =>
-    let mut newContents := #[]
-    for c in contents do
-      match c with
-      | Content.Character s =>
-        newContents := newContents ++ (← splitAround s unicodeToSplit |>.mapM linkify).join
-      | _ => newContents := newContents.push c
-    return ⟨ name, attrs, newContents ⟩
-  where
-    linkify s := do
-      let link? ← nameToLink? s
-      match link? with
-      | some link =>
-        let attributes := Lean.RBMap.empty.insert "href" link
-        return [Content.Element <| Element.Element "a" attributes #[Content.Character s]]
-      | none =>
-        let sHead := s.dropRightWhile (· != '.')
-        let sTail := s.takeRightWhile (· != '.')
-        let link'? ← nameToLink? sTail
-        match link'? with
-        | some link' =>
-          let attributes := Lean.RBMap.empty.insert "href" link'
-          return [
-            Content.Character sHead,
-            Content.Element <| Element.Element "a" attributes #[Content.Character sTail]
-          ]
-        | none =>
-          return [Content.Character s]
-    unicodeToSplit (c : Char) : Bool :=
-      let cats := [
-        Unicode.GeneralCategory.Z, -- separator
-        Unicode.GeneralCategory.C -- other
-      ]
-      cats.any (Unicode.isInGeneralCategory c)
-
-/-- Core function of modifying the cmark rendered docstring html. -/
-partial def modifyElement (element : Element) : HtmlM Element :=
-  match element with
-  | el@(Element.Element name attrs contents) => do
-    -- add id and class to <h_></h_>
-    if name = "h1" ∨ name = "h2" ∨ name = "h3" ∨ name = "h4" ∨ name = "h5" ∨ name = "h6" then
-      addHeadingAttributes el modifyElement
-    -- extend relative href for <a></a>
-    else if name = "a" then
-      extendAnchor el
-    -- auto link for inline <code></code>
-    else if name = "code" then
-      autoLink el
-    -- recursively modify
-    else
-      let newContents ← contents.mapM fun c => match c with
-        | Content.Element e => return Content.Element (← modifyElement e)
-        | _ => pure c
-      return ⟨ name, attrs, newContents ⟩
-
-/-- Convert docstring to Html. -/
-def docStringToHtml (s : String) : HtmlM (Array Html) := do
-  let rendered := CMark.renderHtml s
-  match manyDocument rendered.mkIterator with
-  | Parsec.ParseResult.success _ res =>
-    res.mapM fun x => do return Html.text <| toString (← modifyElement x)
-  | _ => return #[Html.text rendered]
-
-end Output
-end DocGen4

DocGen4/Output/Find.lean

@@ -1,22 +0,0 @@
-import DocGen4.Output.Template
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-open Lean
-
-def find : BaseHtmlM Html := do
-  pure
-    <html lang="en">
-      <head>
-        <link rel="preload" href={s!"{← getRoot}/declarations/declaration-data.bmp"} as="image"/>
-        <script>{s!"const SITE_ROOT={String.quote (← getRoot)};"}</script>
-        <script type="module" async="true" src="./find.js"></script>
-      </head>
-      <body></body>
-    </html>
-
-end Output
-end DocGen4
-

DocGen4/Output/FoundationalTypes.lean

@@ -1,51 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.Inductive
-
-namespace DocGen4.Output
-
-open scoped DocGen4.Jsx
-
-def foundationalTypes : BaseHtmlM Html := templateLiftExtends (baseHtml "Foundational Types") do
-  pure <|
-    <main>
-      <a id="top"></a>
-      <h1>Foundational Types</h1>
-
-      <p>Some of Lean's types are not defined in any Lean source files (even the <code>prelude</code>) since they come from its foundational type theory. This page provides basic documentation for these types.</p>
-      <p>For a more in-depth explanation of Lean's type theory, refer to
-      <a href="https://leanprover.github.io/theorem_proving_in_lean4/dependent_type_theory.html">TPiL</a>.</p>
-      
-      
-      <h2 id="codesort-ucode"><code>Sort u</code></h2>
-      <p><code>Sort u</code> is the type of types in Lean, and <code>Sort u : Sort (u + 1)</code>.</p>
-      {← instancesForToHtml `_builtin_sortu}
-    
-      <h2 id="codetype-ucode"><code>Type u</code></h2>
-      <p><code>Type u</code> is notation for <code>Sort (u + 1)</code>.</p>    
-      {← instancesForToHtml `_builtin_typeu}
-      
-      <h2 id="codepropcode"><code>Prop</code></h2>
-      <p><code>Prop</code> is notation for <code>Sort 0</code>.</p>    
-      {← instancesForToHtml `_builtin_prop}
-    
-      <h2 id="pi-types-codeπ-a--α-β-acode">Pi types, <code>{"(a : α) → β a"}</code></h2>
-      <p>The type of dependent functions is known as a pi type.
-      Non-dependent functions and implications are a special case.</p>
-      <p>Note that these can also be written with the alternative notations:</p>
-      <ul>
-      <li><code>∀ a : α, β a</code>, conventionally used where <code>β a : Prop</code>.</li>
-      <li><code>(a : α) → β a</code></li>
-      <li><code>α → γ</code>, possible only if <code>β a = γ</code> for all <code>a</code>.</li>
-      </ul>
-      <p>Lean also permits ASCII-only spellings of the three variants:</p>
-      <ul>
-      <li><code>forall a : A, B a</code> for <code>{"∀ a : α, β a"}</code></li>
-      <li><code>(a : A) -&gt; B a</code>, for <code>(a : α) → β a</code></li>
-      <li><code>A -&gt; B</code>, for <code>α → β</code></li>
-      </ul>
-      <p>Note that despite not itself being a function, <code>(→)</code> is available as infix notation for
-      <code>{"fun α β, α → β"}</code>.</p>    
-      -- TODO: instances for pi types 
-    </main>
-
-end DocGen4.Output

DocGen4/Output/Index.lean

@@ -1,83 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.Output.ToHtmlFormat
-import DocGen4.Output.Template
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-
-def index : BaseHtmlM Html := do templateExtends (baseHtml "Index") <|
-  pure <|
-    <main>
-      <a id="top"></a>
-      <h1>Bookshelf</h1>
-      <p>
-        A study of the books listed below. Most proofs are conducted in LaTeX.
-        Where feasible, theorems are also formally proven in
-        <a target="_blank" href="https://leanprover.github.io/">Lean</a>.
-      </p>
-
-      <h2>In Progress</h2>
-      <ul>
-        <li>Apostol, Tom M. Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. 2nd ed. Vol. 1. 2 vols. Wiley, 1991.</li>
-        <li>Enderton, Herbert B. A Mathematical Introduction to Logic. 2nd ed. San Diego: Harcourt/Academic Press, 2001.</li>
-        <li>Enderton, Herbert B. Elements of Set Theory. New York: Academic Press, 1977.</li>
-      </ul>
-
-      <h2>Complete</h2>
-      <ul>
-        <li>Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.</li>
-      </ul>
-
-      <h2>Pending</h2>
-      <ul>
-        <li>Axler, Sheldon. Linear Algebra Done Right. Undergraduate Texts in Mathematics. Cham: Springer International Publishing, 2015.</li>
-        <li>Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. 3rd ed. Cambridge, Mass: MIT Press, 2009.</li>
-        <li>Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.</li>
-        <li>Gustedt, Jens. Modern C. Shelter Island, NY: Manning Publications Co, 2020.</li>
-        <li>Ross, Sheldon. A First Course in Probability Theory. 8th ed. Pearson Prentice Hall, n.d.</li>
-        <li>Smullyan, Raymond M. To Mock a Mockingbird: And Other Logic Puzzles Including an Amazing Adventure in Combinatory Logic. Oxford: Oxford university press, 2000.</li>
-      </ul>
-
-      <h2>Legend</h2>
-      <p>
-        A color/symbol code is used on generated PDF headers to indicate their
-        status:
-        <ul>
-          <li>
-            <span style="color:darkgray">Dark gray statements </span> are
-            reserved for definitions and axioms that have been encoded in LaTeX.
-            A reference to a definition in Lean may also be provided.
-          </li>
-          <li>
-            <span style="color:teal">Teal statements </span> are reserved for
-            statements, theorems, lemmas, etc. that have been proven in LaTeX
-            and have a corresponding proof in Lean.
-          </li>
-          <li>
-            <span style="color:olive">Olive statements </span> are reserved for
-            statements, theorems, lemmas, etc. that have been proven in LaTeX.
-            A reference to a statement in Lean may also be provided.
-          </li>
-          <li>
-            <span style="color:fuchsia">Fuchsia statements </span> are reserved
-            for statements, theorems, lemmas, etc. that have been proven in
-            LaTeX and <i>will </i> have a corresponding proof in Lean.
-          </li>
-          <li>
-            <span style="color:maroon">Maroon </span> serves as a catch-all for
-            statements that don't fit the above categorizations. Incomplete
-            definitions, statements without proof, etc. belong here.
-          </li>
-        </ul>
-      </p>
-      <p>This was built using Lean 4 at commit <a href={s!"https://github.com/leanprover/lean4/tree/{Lean.githash}"}>{Lean.githash}</a></p>
-    </main>
-
-end Output
-end DocGen4

DocGen4/Output/Inductive.lean

@@ -1,39 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.DocString
-import DocGen4.Process
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-open Lean
-
-def instancesForToHtml (typeName : Name) : BaseHtmlM Html := do
-  pure
-    <details «class»="instances">
-        <summary>Instances For</summary>
-        <ul id={s!"instances-for-list-{typeName}"} class="instances-for-list"></ul>
-    </details>
-
-def ctorToHtml (c : Process.NameInfo) : HtmlM Html := do
-  let shortName := c.name.componentsRev.head!.toString
-  let name := c.name.toString
-  if let some doc := c.doc then
-    let renderedDoc ← docStringToHtml doc
-    pure
-      <li class="constructor" id={name}>
-        {shortName} : [← infoFormatToHtml c.type]
-        <div class="inductive_ctor_doc">[renderedDoc]</div>
-      </li>
-  else
-    pure
-      <li class="constructor" id={name}>
-        {shortName} : [← infoFormatToHtml c.type]
-      </li>
-
-def inductiveToHtml (i : Process.InductiveInfo) : HtmlM (Array Html) := do
-  let constructorsHtml := <ul class="constructors">[← i.ctors.toArray.mapM ctorToHtml]</ul>
-  return #[constructorsHtml]
-
-end Output
-end DocGen4

DocGen4/Output/Instance.lean

@@ -1,8 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.Definition
-
-namespace DocGen4
-namespace Output
-
-end Output
-end DocGen4

DocGen4/Output/Module.lean

@@ -1,216 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.Output.Template
-import DocGen4.Output.Inductive
-import DocGen4.Output.Structure
-import DocGen4.Output.Class
-import DocGen4.Output.Definition
-import DocGen4.Output.Instance
-import DocGen4.Output.ClassInductive
-import DocGen4.Output.DocString
-import DocGen4.Process
-import Lean.Data.Xml.Parser
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-open Lean Process
-
-/--
-Render an `Arg` as HTML, adding opacity effects etc. depending on what
-type of binder it has.
--/
-def argToHtml (arg : Arg) : HtmlM Html := do
-  let (l, r, implicit) := match arg.binderInfo with
-  | BinderInfo.default => ("(", ")", false)
-  | BinderInfo.implicit => ("{", "}", true)
-  | BinderInfo.strictImplicit => ("⦃", "⦄", true)
-  | BinderInfo.instImplicit => ("[", "]", true)
-  let mut nodes := #[Html.text s!"{l}{arg.name.toString} : "]
-  nodes := nodes.append (← infoFormatToHtml arg.type)
-  nodes := nodes.push r
-  let inner := <span class="fn">[nodes]</span>
-  let html := Html.element "span" false #[("class", "decl_args")] #[inner]
-  if implicit then
-    return <span class="impl_arg">{html}</span>
-  else
-    return html
-
-/--
-Render the structures this structure extends from as HTML so it can be
-added to the top level.
--/
-def structureInfoHeader (s : Process.StructureInfo) : HtmlM (Array Html) := do
-  let mut nodes := #[]
-  if s.parents.size > 0 then
-    nodes := nodes.push <span class="decl_extends">extends</span>
-    let mut parents := #[]
-    for parent in s.parents do
-      let link ← declNameToHtmlBreakWithinLink parent
-      let inner := <span class="fn">{link}</span>
-      let html:= Html.element "span" false #[("class", "decl_parent")] #[inner]
-      parents := parents.push html
-    nodes := nodes.append (parents.toList.intersperse (Html.text ", ")).toArray
-  return nodes
-
-/--
-Render the general header of a declaration containing its declaration type
-and name.
--/
-def docInfoHeader (doc : DocInfo) : HtmlM Html := do
-  let mut nodes := #[]
-  nodes := nodes.push <| Html.element "span" false #[("class", "decl_kind")] #[doc.getKindDescription]
-  nodes := nodes.push
-    <span class="decl_name">
-      {← declNameToHtmlBreakWithinLink doc.getName}
-    </span>
-  for arg in doc.getArgs do
-    nodes := nodes.push (← argToHtml arg)
-
-  match doc with
-  | DocInfo.structureInfo i => nodes := nodes.append (← structureInfoHeader i)
-  | DocInfo.classInfo i => nodes := nodes.append (← structureInfoHeader i)
-  | _ => nodes := nodes
-
-  nodes := nodes.push <| Html.element "span" true #[("class", "decl_args")] #[" :"]
-  nodes := nodes.push <div class="decl_type">[← infoFormatToHtml doc.getType]</div>
-  return <div class="decl_header"> [nodes] </div>
-
-/--
-The main entry point for rendering a single declaration inside a given module.
--/
-def docInfoToHtml (module : Name) (doc : DocInfo) : HtmlM Html := do
-  -- basic info like headers, types, structure fields, etc.
-  let docInfoHtml ← match doc with
-  | DocInfo.inductiveInfo i => inductiveToHtml i
-  | DocInfo.structureInfo i => structureToHtml i
-  | DocInfo.classInfo i => classToHtml i
-  | DocInfo.classInductiveInfo i => classInductiveToHtml i
-  | _ => pure #[]
-  -- rendered doc stirng
-  let docStringHtml ← match doc.getDocString with
-  | some s => docStringToHtml s
-  | none => pure #[]
-  -- extra information like equations and instances
-  let extraInfoHtml ← match doc with
-  | DocInfo.classInfo i => pure #[← classInstancesToHtml i.name]
-  | DocInfo.definitionInfo i => pure ((← equationsToHtml i) ++ #[← instancesForToHtml i.name])
-  | DocInfo.instanceInfo i => equationsToHtml i.toDefinitionInfo
-  | DocInfo.classInductiveInfo i => pure #[← classInstancesToHtml i.name]
-  | DocInfo.inductiveInfo i => pure #[← instancesForToHtml i.name]
-  | DocInfo.structureInfo i => pure #[← instancesForToHtml i.name]
-  | _ => pure #[]
-  let attrs := doc.getAttrs
-  let attrsHtml :=
-    if attrs.size > 0 then
-      let attrStr := "@[" ++ String.intercalate ", " doc.getAttrs.toList ++ "]"
-      #[Html.element "div" false #[("class", "attributes")] #[attrStr]]
-    else
-      #[]
-  let leanInkHtml :=
-    if ← leanInkEnabled? then
-      #[
-        <div class="ink_link">
-          <a href={← declNameToInkLink doc.getName}>ink</a>
-        </div>
-      ]
-    else
-      #[]
-
-  pure
-    <div class="decl" id={doc.getName.toString}>
-      <div class={doc.getKind}>
-        <div class="gh_link">
-          <a href={← getSourceUrl module doc.getDeclarationRange}>source</a>
-        </div>
-        [leanInkHtml]
-        [attrsHtml]
-        {← docInfoHeader doc}
-        [docInfoHtml]
-        [docStringHtml]
-        [extraInfoHtml]
-      </div>
-    </div>
-
-/--
-Rendering a module doc string, that is the ones with an ! after the opener
-as HTML.
--/
-def modDocToHtml (mdoc : ModuleDoc) : HtmlM Html := do
-  pure
-    <div class="mod_doc">
-      [← docStringToHtml mdoc.doc]
-    </div>
-
-/--
-Render a module member, that is either a module doc string or a declaration
-as HTML.
--/
-def moduleMemberToHtml (module : Name) (member : ModuleMember) : HtmlM Html := do
-  match member with
-  | ModuleMember.docInfo d => docInfoToHtml module d
-  | ModuleMember.modDoc d => modDocToHtml d
-
-def declarationToNavLink (module : Name) : Html :=
-  <div class="nav_link">
-    <a class="break_within" href={s!"#{module.toString}"}>
-      [breakWithin module.toString]
-    </a>
-  </div>
-
-/--
-Returns the list of all imports this module does.
--/
-def getImports (module : Name) : HtmlM (Array Name) := do
-  let res ← getResult
-  return res.moduleInfo.find! module |>.imports
-
-/--
-Sort the list of all modules this one is importing, linkify it
-and return the HTML.
--/
-def importsHtml (moduleName : Name) : HtmlM (Array Html) := do
-  let imports := (← getImports moduleName).qsort Name.lt
-  imports.mapM (fun i => do return <li>{← moduleToHtmlLink i}</li>)
-
-/--
-Render the internal nav bar (the thing on the right on all module pages).
--/
-def internalNav (members : Array Name) (moduleName : Name) : HtmlM Html := do
-  pure
-    <nav class="internal_nav">
-      <h3><a class="break_within" href="#top">[breakWithin moduleName.toString]</a></h3>
-      <p class="gh_nav_link"><a href={← getSourceUrl moduleName none}>source</a></p>
-      <div class="imports">
-        <details>
-          <summary>Imports</summary>
-          <ul>
-            [← importsHtml moduleName]
-          </ul>
-        </details>
-        <details>
-          <summary>Imported by</summary>
-          <ul id={s!"imported-by-{moduleName}"} class="imported-by-list"> </ul>
-        </details>
-      </div>
-      [members.map declarationToNavLink]
-    </nav>
-
-/--
-The main entry point to rendering the HTML for an entire module.
--/
-def moduleToHtml (module : Process.Module) : HtmlM Html := withTheReader SiteBaseContext (setCurrentName module.name) do
-  let relevantMembers := module.members.filter Process.ModuleMember.shouldRender
-  let memberDocs ← relevantMembers.mapM (moduleMemberToHtml module.name)
-  let memberNames := filterDocInfo relevantMembers |>.map DocInfo.getName
-  templateLiftExtends (baseHtmlGenerator module.name.toString) <| pure #[
-    ← internalNav memberNames module.name,
-    Html.element "main" false #[] memberDocs
-  ]
-
-end Output
-end DocGen4

DocGen4/Output/Navbar.lean

@@ -1,111 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-import DocGen4.Output.ToHtmlFormat
-import DocGen4.Output.Base
-
-namespace DocGen4
-namespace Output
-
-open Lean
-open scoped DocGen4.Jsx
-
-def moduleListFile (file : NameExt) : BaseHtmlM Html := do
-  let contents :=
-    if file.ext == .pdf then
-      <span>{s!"🗎 {file.getString!} (<a class=\"pdf\" target=\"_blank\" href={← moduleNameExtToLink file}>pdf</a>)"}</span>
-    else
-      <a href={← moduleNameExtToLink file}>{file.getString!}</a>
-  return <div class={if (← getCurrentName) == file.name then "nav_link visible" else "nav_link"}>
-    {contents}
-  </div>
-
-/--
-Build the HTML tree representing the module hierarchy.
--/
-partial def moduleListDir (h : Hierarchy) : BaseHtmlM Html := do
-  let children := Array.mk (h.getChildren.toList.map Prod.snd)
-  let nodes ← children.mapM (fun c =>
-    if c.getChildren.toList.length != 0 then
-      moduleListDir c
-    else if Hierarchy.isFile c && c.getChildren.toList.length = 0 then
-      moduleListFile (Hierarchy.getNameExt c)
-    else
-      pure ""
-  )
-  let moduleLink ← moduleNameToHtmlLink h.getName
-  let summary :=
-    if h.isFile then
-      <summary>{s!"{h.getName.getString!} ({<a href={← moduleNameToHtmlLink h.getName}>file</a>})"} </summary>
-    else
-      <summary>{h.getName.getString!}</summary>
-
-  pure
-    <details class="nav_sect" "data-path"={moduleLink} [if (← getCurrentName).any (h.getName.isPrefixOf ·) then #[("open", "")] else #[]]>
-      {summary}
-      [nodes]
-    </details>
-
-/--
-Return a list of top level modules, linkified and rendered as HTML
--/
-def moduleList : BaseHtmlM Html := do
-  let hierarchy ← getHierarchy
-  let mut list := Array.empty
-  for (_, cs) in hierarchy.getChildren do
-    list := list.push <| ← moduleListDir cs
-  return <div class="module_list">[list]</div>
-
-/--
-The main entry point to rendering the navbar on the left hand side.
--/
-def navbar : BaseHtmlM Html := do
-  pure
-    <html lang="en">
-      <head>
-        [← baseHtmlHeadDeclarations]
-
-        <script type="module" src={s!"{← getRoot}nav.js"}></script>
-        <script type="module" src={s!"{← getRoot}color-scheme.js"}></script>
-        <base target="_parent" />
-      </head>
-
-      <body>
-        <div class="navframe">
-        <nav class="nav">
-          <h3>General documentation</h3>
-          <div class="nav_link"><a href={s!"{← getRoot}"}>index</a></div>
-          <div class="nav_link"><a href={s!"{← getRoot}foundational_types.html"}>foundational types</a></div>
-          /-
-          TODO: Add these in later
-          <div class="nav_link"><a href={s!"{← getRoot}tactics.html"}>tactics</a></div>
-          <div class="nav_link"><a href={s!"{← getRoot}commands.html"}>commands</a></div>
-          <div class="nav_link"><a href={s!"{← getRoot}hole_commands.html"}>hole commands</a></div>
-          <div class="nav_link"><a href={s!"{← getRoot}attributes.html"}>attributes</a></div>
-          <div class="nav_link"><a href={s!"{← getRoot}notes.html"}>notes</a></div>
-          <div class="nav_link"><a href={s!"{← getRoot}references.html"}>references</a></div>
-          -/
-          <h3>Library</h3>
-          {← moduleList}
-          <div id="settings" hidden="hidden">
-            -- `input` is a void tag, but can be self-closed to make parsing easier.
-            <h3>Color scheme</h3>
-            <form id="color-theme-switcher">
-                <label for="color-theme-dark">
-                    <input type="radio" name="color_theme" id="color-theme-dark" value="dark" autocomplete="off"/>dark</label>
-                <label for="color-theme-system" title="Match system theme settings">
-                    <input type="radio" name="color_theme" id="color-theme-system" value="system" autocomplete="off"/>system</label>
-                <label for="color-theme-light">
-                    <input type="radio" name="color_theme" id="color-theme-light" value="light" autocomplete="off"/>light</label>
-            </form>
-          </div>
-        </nav>
-        </div>
-      </body>
-    </html>
-
-end Output
-end DocGen4

DocGen4/Output/NotFound.lean

@@ -1,26 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.Output.ToHtmlFormat
-import DocGen4.Output.Template
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-
-/--
-Render the 404 page.
--/
-def notFound : BaseHtmlM Html := do templateExtends (baseHtml "404") <|
-  pure <|
-    <main>
-      <h1>404 Not Found</h1>
-      <p> Unfortunately, the page you were looking for is no longer here. </p>
-      <div id="howabout"></div>
-    </main>
-
-end Output
-end DocGen4

DocGen4/Output/Search.lean

@@ -1,48 +0,0 @@
-/-
-Copyright (c) 2023 Jeremy Salwen. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Jeremy Salwen
--/
-import DocGen4.Output.ToHtmlFormat
-import DocGen4.Output.Template
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-
-def search : BaseHtmlM Html := do templateExtends (baseHtml "Search") <|
-  pure <|
-    <main>
-      <h1> Search Results </h1>
-      <label for="search_page_query">Query:</label>
-      <input id="search_page_query" />
-      <div id="kinds">
-        Allowed Kinds:
-        <input type="checkbox" id="def_checkbox" class="kind_checkbox" value="def" checked="checked" />
-        <label for="def_checkbox">def</label>
-        <input type="checkbox" id="theorem_checkbox" class="kind_checkbox" value="theorem" checked="checked" />
-        <label for="theorem_checkbox">theorem</label>
-        <input type="checkbox" id="inductive_checkbox" class="kind_checkbox" value="inductive" checked="checked" />
-        <label for="inductive_checkbox">inductive</label>
-        <input type="checkbox" id="structure_checkbox" class="kind_checkbox" value="structure" checked="checked" />
-        <label for="structure_checkbox">structure</label>
-        <input type="checkbox" id="class_checkbox" class="kind_checkbox" value="class" checked="checked" />
-        <label for="class_checkbox">class</label>
-        <input type="checkbox" id="instance_checkbox" class="kind_checkbox" value="instance" checked="checked" />
-        <label for="instance_checkbox">instance</label>
-        <input type="checkbox" id="axiom_checkbox" class="axiom_checkbox" value="axiom" checked="checked" />
-        <label for="axiom_checkbox">axiom</label>
-        <input type="checkbox" id="opaque_checkbox" class="kind_checkbox" value="opaque" checked="checked" />
-        <label for="opaque_checkbox">opaque</label>
-      </div>
-      
-      <script>
-        document.getElementById("search_page_query").value = new URL(window.location.href).searchParams.get("q")
-      </script>
-      <div id="search_results">
-      </div>
-    </main>
-
-end Output
-end DocGen4

DocGen4/Output/SourceLinker.lean

@@ -1,103 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-import Lake.Load
-
-namespace DocGen4.Output.SourceLinker
-
-open Lean
-
-/--
-Turns a Github git remote URL into an HTTPS Github URL.
-Three link types from git supported:
-- https://github.com/org/repo
-- https://github.com/org/repo.git
-- git@github.com:org/repo.git
-
-TODO: This function is quite brittle and very Github specific, we can
-probably do better.
--/
-def getGithubBaseUrl (gitUrl : String) : String := Id.run do
-  let mut url := gitUrl
-  if url.startsWith "git@" then
-    url := url.drop 15
-    url := url.dropRight 4
-    return s!"https://github.com/{url}"
-  else if url.endsWith ".git" then
-    return url.dropRight 4
-  else
-    return url
-
-/--
-Obtain the Github URL of a project by parsing the origin remote.
--/
-def getProjectGithubUrl (directory : System.FilePath := "." ) : IO String := do
-  let out ← IO.Process.output {
-    cmd := "git",
-    args := #["remote", "get-url", "origin"],
-    cwd := directory
-  }
-  if out.exitCode != 0 then
-    throw <| IO.userError <| "git exited with code " ++ toString out.exitCode
-  return out.stdout.trimRight
-
-/--
-Obtain the git commit hash of the project that is currently getting analyzed.
--/
-def getProjectCommit (directory : System.FilePath := "." ) : IO String := do
-  let out ← IO.Process.output {
-    cmd := "git",
-    args := #["rev-parse", "HEAD"]
-    cwd := directory
-  }
-  if out.exitCode != 0 then
-    throw <| IO.userError <| "git exited with code " ++ toString out.exitCode
-  return out.stdout.trimRight
-
-/--
-Given a lake workspace with all the dependencies as well as the hash of the
-compiler release to work with this provides a function to turn names of
-declarations into (optionally positional) Github URLs.
--/
-def sourceLinker (ws : Lake.Workspace) : IO (Name → Option DeclarationRange → String) := do
-  let leanHash := ws.lakeEnv.lean.githash
-  -- Compute a map from package names to source URL
-  let mut gitMap := Lean.mkHashMap
-  let projectBaseUrl := getGithubBaseUrl (← getProjectGithubUrl)
-  let projectCommit ← getProjectCommit
-  gitMap := gitMap.insert ws.root.name (projectBaseUrl, projectCommit)
-  let manifest ← Lake.Manifest.loadOrEmpty ws.root.manifestFile
-      |>.run (Lake.MonadLog.eio .normal)
-      |>.toIO (fun _ => IO.userError "Failed to load lake manifest")
-  for pkg in manifest.entryArray do
-    match pkg with
-    | .git _ _ _ url rev .. => gitMap := gitMap.insert pkg.name (getGithubBaseUrl url, rev)
-    | .path _ _ _ path =>
-      let pkgBaseUrl := getGithubBaseUrl (← getProjectGithubUrl path)
-      let pkgCommit ← getProjectCommit path
-      gitMap := gitMap.insert pkg.name (pkgBaseUrl, pkgCommit)
-
-  return fun module range =>
-    let parts := module.components.map Name.toString
-    let path := (parts.intersperse "/").foldl (· ++ ·) ""
-    let root := module.getRoot
-    let basic := if root == `Lean ∨ root == `Init then
-      s!"https://github.com/leanprover/lean4/blob/{leanHash}/src/{path}.lean"
-    else if root == `Lake then
-      s!"https://github.com/leanprover/lean4/blob/{leanHash}/src/lake/{path}.lean"
-    else
-      match ws.packageArray.find? (·.isLocalModule module) with
-      | some pkg =>
-        match gitMap.find? pkg.name with
-        | some (baseUrl, commit) => s!"{baseUrl}/blob/{commit}/{path}.lean"
-        | none => "https://example.com"
-      | none => "https://example.com"
-
-    match range with
-    | some range => s!"{basic}#L{range.pos.line}-L{range.endPos.line}"
-    | none => basic
-
-end DocGen4.Output.SourceLinker

DocGen4/Output/Structure.lean

@@ -1,51 +0,0 @@
-import DocGen4.Output.Template
-import DocGen4.Output.DocString
-import DocGen4.Process
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-open Lean
-
-/--
-Render a single field consisting of its documentation, its name and its type as HTML.
--/
-def fieldToHtml (f : Process.NameInfo) : HtmlM Html := do
-  let shortName := f.name.componentsRev.head!.toString
-  let name := f.name.toString
-  if let some doc := f.doc then
-    let renderedDoc ← docStringToHtml doc
-    pure
-      <li id={name} class="structure_field">
-        <div class="structure_field_info">{s!"{shortName} "} : [← infoFormatToHtml f.type]</div>
-        <div class="structure_field_doc">[renderedDoc]</div>
-      </li>
-  else
-    pure
-      <li id={name} class="structure_field">
-        <div class="structure_field_info">{s!"{shortName} "} : [← infoFormatToHtml f.type]</div>
-      </li>
-
-/--
-Render all information about a structure as HTML.
--/
-def structureToHtml (i : Process.StructureInfo) : HtmlM (Array Html) := do
-  let structureHtml :=
-    if Name.isSuffixOf `mk i.ctor.name then
-      (<ul class="structure_fields" id={i.ctor.name.toString}>
-        [← i.fieldInfo.mapM fieldToHtml]
-      </ul>)
-    else
-      let ctorShortName := i.ctor.name.componentsRev.head!.toString
-      (<ul class="structure_ext">
-        <li id={i.ctor.name.toString} class="structure_ext_ctor">{s!"{ctorShortName} "} :: (</li>
-        <ul class="structure_ext_fields">
-          [← i.fieldInfo.mapM fieldToHtml]
-        </ul>
-        <li class="structure_ext_ctor">)</li>
-      </ul>)
-  return #[structureHtml]
-
-end Output
-end DocGen4

DocGen4/Output/Template.lean

@@ -1,70 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import DocGen4.Output.ToHtmlFormat
-import DocGen4.Output.Navbar
-
-namespace DocGen4
-namespace Output
-
-open scoped DocGen4.Jsx
-
-/--
-The HTML template used for all pages.
--/
-def baseHtmlGenerator (title : String) (site : Array Html) : BaseHtmlM Html := do
-  let moduleConstant :=
-    if let some module := ← getCurrentName then
-      #[<script>{s!"const MODULE_NAME={String.quote module.toString};"}</script>]
-    else
-      #[]
-  pure
-    <html lang="en">
-      <head>
-        [← baseHtmlHeadDeclarations]
-
-        <title>{title}</title>
-        <script defer="true" src={s!"{← getRoot}mathjax-config.js"}></script>
-        <script defer="true" src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
-        <script defer="true" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
-
-        <script>{s!"const SITE_ROOT={String.quote (← getRoot)};"}</script>
-        [moduleConstant]
-        <script type="module" src={s!"{← getRoot}search.js"}></script>
-        <script type="module" src={s!"{← getRoot}how-about.js"}></script>
-        <script type="module" src={s!"{← getRoot}instances.js"}></script>
-        <script type="module" src={s!"{← getRoot}importedBy.js"}></script>
-      </head>
-
-      <body>
-
-        <input id="nav_toggle" type="checkbox"/>
-
-        <header>
-          <h1><label for="nav_toggle"></label>Documentation</h1>
-          <p class="header_filename break_within">[breakWithin title]</p>
-          <form action="https://google.com/search" method="get" id="search_form">
-            <input type="hidden" name="sitesearch" value="https://leanprover-community.github.io/mathlib4_docs"/>
-            <input type="text" name="q" autocomplete="off"/>&#32;
-            <button id="search_button" onclick={s!"javascript: form.action='{← getRoot}search.html';"}>Search</button>
-            <button>Google site search</button>
-          </form>
-        </header>
-
-        [site]
-
-        <nav class="nav">
-          <iframe src={s!"{← getRoot}navbar.html"} class="navframe" frameBorder="0"></iframe>
-        </nav>
-      </body>
-    </html>
-
-/--
-A comfortability wrapper around `baseHtmlGenerator`.
--/
-def baseHtml (title : String) (site : Html) : BaseHtmlM Html := baseHtmlGenerator title #[site]
-
-end Output
-end DocGen4

DocGen4/Output/ToHtmlFormat.lean

@@ -1,149 +0,0 @@
-/-
-Copyright (c) 2021 Wojciech Nawrocki. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-
-Authors: Wojciech Nawrocki, Sebastian Ullrich, Henrik Böving
--/
-import Lean.Data.Json
-import Lean.Parser
-
-/-! This module defines:
-- a representation of HTML trees
-- together with a JSX-like DSL for writing them
-- and widget support for visualizing any type as HTML. -/
-
-namespace DocGen4
-
-open Lean
-
-inductive Html where
-  -- TODO(WN): it's nameless for shorter JSON; re-add names when we have deriving strategies for From/ToJson
-  -- element (tag : String) (flatten : Bool) (attrs : Array HtmlAttribute) (children : Array Html)
-  | element : String → Bool → Array (String × String) → Array Html → Html
-  | text : String → Html
-  deriving Repr, BEq, Inhabited, FromJson, ToJson
-
-instance : Coe String Html :=
-  ⟨Html.text⟩
-
-namespace Html
-
-def attributesToString (attrs : Array (String × String)) :String :=
-  attrs.foldl (fun acc (k, v) => acc ++ " " ++ k ++ "=\"" ++ v ++ "\"") ""
-
--- TODO: Termination proof
-partial def toStringAux : Html → String
-| element tag false attrs #[text s] => s!"<{tag}{attributesToString attrs}>{s}</{tag}>\n"
-| element tag false attrs #[child] => s!"<{tag}{attributesToString attrs}>\n{child.toStringAux}</{tag}>\n"
-| element tag false attrs children => s!"<{tag}{attributesToString attrs}>\n{children.foldl (· ++ toStringAux ·) ""}</{tag}>\n"
-| element tag true attrs children => s!"<{tag}{attributesToString attrs}>{children.foldl (· ++ toStringAux ·) ""}</{tag}>"
-| text s => s
-
-def toString (html : Html) : String :=
-  html.toStringAux.trimRight
-
-instance : ToString Html :=
-  ⟨toString⟩
-
-partial def textLength : Html → Nat
-| text s => s.length
-| element _ _ _ children =>
-  let lengths := children.map textLength
-  lengths.foldl Nat.add 0
-
-def escapePairs : Array (String × String) :=
-  #[
-    ("&", "&amp"),
-    ("<", "&lt"),
-    (">", "&gt"),
-    ("\"", "&quot")
-  ]
-
-def escape (s : String) : String :=
-  escapePairs.foldl (fun acc (o, r) => acc.replace o r) s
-
-end Html
-
-namespace Jsx
-open Parser PrettyPrinter
-
-declare_syntax_cat jsxElement
-declare_syntax_cat jsxChild
-
--- JSXTextCharacter : SourceCharacter but not one of {, <, > or }
-def jsxText : Parser :=
-  withAntiquot (mkAntiquot "jsxText" `jsxText) {
-    fn := fun c s =>
-      let startPos := s.pos
-      let s := takeWhile1Fn (not ∘ "[{<>}]$".contains) "expected JSX text" c s
-      mkNodeToken `jsxText startPos c s }
-
-@[combinator_formatter DocGen4.Jsx.jsxText] def jsxText.formatter : Formatter := pure ()
-@[combinator_parenthesizer DocGen4.Jsx.jsxText] def jsxText.parenthesizer : Parenthesizer := pure ()
-
-syntax jsxAttrName := rawIdent <|> str
-syntax jsxAttrVal := str <|> group("{" term "}")
-syntax jsxSimpleAttr := jsxAttrName "=" jsxAttrVal
-syntax jsxAttrSpread := "[" term "]"
-syntax jsxAttr := jsxSimpleAttr <|> jsxAttrSpread
-
-syntax "<" rawIdent jsxAttr* "/>" : jsxElement
-syntax "<" rawIdent jsxAttr* ">" jsxChild* "</" rawIdent ">" : jsxElement
-
-syntax jsxText      : jsxChild
-syntax "{" term "}" : jsxChild
-syntax "[" term "]" : jsxChild
-syntax jsxElement   : jsxChild
-
-scoped syntax:max jsxElement : term
-
-def translateAttrs (attrs : Array (TSyntax `DocGen4.Jsx.jsxAttr)) : MacroM (TSyntax `term) := do
-  let mut as ← `(#[])
-  for attr in attrs.map TSyntax.raw do
-    as ← match attr with
-    | `(jsxAttr| $n:jsxAttrName=$v:jsxAttrVal) =>
-      let n ← match n with
-        | `(jsxAttrName| $n:str) => pure n
-        | `(jsxAttrName| $n:ident) => pure <| quote (toString n.getId)
-        | _ => Macro.throwUnsupported
-      let v ← match v with
-        | `(jsxAttrVal| {$v}) => pure v
-        | `(jsxAttrVal| $v:str) => pure v
-        | _ => Macro.throwUnsupported
-      `(($as).push ($n, ($v : String)))
-    | `(jsxAttr| [$t]) => `($as ++ ($t : Array (String × String)))
-    | _ => Macro.throwUnsupported
-  return as
-
-private def htmlHelper (n : Syntax) (children : Array Syntax) (m : Syntax) : MacroM (String × (TSyntax `term)):= do
-  unless n.getId == m.getId do
-    withRef m <| Macro.throwError s!"Leading and trailing part of tags don't match: '{n}', '{m}'"
-  let mut cs ← `(#[])
-  for child in children do
-    cs ← match child with
-    | `(jsxChild|$t:jsxText)    => `(($cs).push (Html.text $(quote t.raw[0]!.getAtomVal)))
-    -- TODO(WN): elab as list of children if type is `t Html` where `Foldable t`
-    | `(jsxChild|{$t})          => `(($cs).push ($t : Html))
-    | `(jsxChild|[$t])          => `($cs ++ ($t : Array Html))
-    | `(jsxChild|$e:jsxElement) => `(($cs).push ($e:jsxElement : Html))
-    | _                         => Macro.throwUnsupported
-  let tag := toString n.getId
-  pure <| (tag, cs)
-
-macro_rules
-  | `(<$n $attrs* />) => do
-    let kind := quote (toString n.getId)
-    let attrs ← translateAttrs attrs
-    `(Html.element $kind true $attrs #[])
-  | `(<$n $attrs* >$children*</$m>) => do
-    let (tag, children) ← htmlHelper n children m
-    `(Html.element $(quote tag) true $(← translateAttrs attrs) $children)
-
-end Jsx
-
-/-- A type which implements `ToHtmlFormat` will be visualized
-as the resulting HTML in editors which support it. -/
-class ToHtmlFormat (α : Type u) where
-  formatHtml : α → Html
-
-end DocGen4

DocGen4/Output/ToJson.lean

@@ -1,126 +0,0 @@
-import Lean
-import DocGen4.Process
-import DocGen4.Output.Base
-import DocGen4.Output.Module
-import Lean.Data.RBMap
-
-namespace DocGen4.Output
-
-open Lean
-
-structure JsonDeclarationInfo where
-  name : String
-  kind : String
-  doc : String
-  docLink : String
-  sourceLink : String
-  line : Nat
-  deriving FromJson, ToJson
-
-structure JsonDeclaration where
-  info : JsonDeclarationInfo
-  header : String
-deriving FromJson, ToJson
-
-structure JsonInstance where
-  name : String
-  className : String
-  typeNames : Array String
-  deriving FromJson, ToJson
-
-structure JsonModule where
-  name : String
-  declarations : List JsonDeclaration
-  instances : Array JsonInstance
-  imports : Array String
-  deriving FromJson, ToJson
-
-structure JsonHeaderIndex where
-  headers : List (String × String) := []
-
-structure JsonIndex where
-  declarations : List (String × JsonDeclarationInfo) := []
-  instances : HashMap String (RBTree String Ord.compare) := .empty
-  importedBy : HashMap String (Array String) := .empty
-  modules : List (String × String) := []
-  instancesFor : HashMap String (RBTree String Ord.compare) := .empty
-
-instance : ToJson JsonHeaderIndex where
-  toJson idx := Json.mkObj <| idx.headers.map (fun (k, v) => (k, toJson v))
-
-instance : ToJson JsonIndex where
-  toJson idx := Id.run do
-    let jsonDecls := Json.mkObj <| idx.declarations.map (fun (k, v) => (k, toJson v))
-    let jsonInstances := Json.mkObj <| idx.instances.toList.map (fun (k, v) => (k, toJson v.toArray))
-    let jsonImportedBy := Json.mkObj <| idx.importedBy.toList.map (fun (k, v) => (k, toJson v))
-    let jsonModules := Json.mkObj <| idx.modules.map (fun (k, v) => (k, toJson v))
-    let jsonInstancesFor := Json.mkObj <| idx.instancesFor.toList.map (fun (k, v) => (k, toJson v.toArray))
-    let finalJson := Json.mkObj [
-      ("declarations", jsonDecls),
-      ("instances", jsonInstances),
-      ("importedBy", jsonImportedBy),
-      ("modules", jsonModules),
-      ("instancesFor", jsonInstancesFor)
-    ]
-    return finalJson
-
-def JsonHeaderIndex.addModule (index : JsonHeaderIndex) (module : JsonModule) : JsonHeaderIndex :=
-  let merge idx decl := { idx with headers := (decl.info.name, decl.header) :: idx.headers }
-  module.declarations.foldl merge index
-
-def JsonIndex.addModule (index : JsonIndex) (module : JsonModule) : BaseHtmlM JsonIndex := do
-  let mut index := index
-  let newModule := (module.name, ← moduleNameToHtmlLink (String.toName module.name))
-  let newDecls := module.declarations.map (fun d => (d.info.name, d.info))
-  index := { index with
-    modules := newModule :: index.modules
-    declarations := newDecls ++ index.declarations
-  }
-  -- TODO: In theory one could sort instances and imports by name and batch the writes
-  for inst in module.instances do
-    let mut insts := index.instances.findD inst.className {}
-    insts := insts.insert inst.name
-    index := { index with instances := index.instances.insert inst.className insts }
-    for typeName in inst.typeNames do
-      let mut instsFor := index.instancesFor.findD typeName {}
-      instsFor := instsFor.insert inst.name
-      index := { index with instancesFor := index.instancesFor.insert typeName instsFor }
-
-  for imp in module.imports do
-    let mut impBy := index.importedBy.findD imp #[]
-    impBy := impBy.push module.name
-    index := { index with importedBy := index.importedBy.insert imp impBy }
-  return index
-
-def DocInfo.toJson (module : Name) (info : Process.DocInfo) : HtmlM JsonDeclaration := do
-  let name := info.getName.toString
-  let kind := info.getKind
-  let doc := info.getDocString.getD ""
-  let docLink ← declNameToLink info.getName
-  let sourceLink ← getSourceUrl module info.getDeclarationRange
-  let line := info.getDeclarationRange.pos.line
-  let header := (← docInfoHeader info).toString
-  let info := { name, kind, doc, docLink, sourceLink, line }
-  return { info, header }
-
-def Process.Module.toJson (module : Process.Module) : HtmlM Json := do
-    let mut jsonDecls := []
-    let mut instances := #[]
-    let declInfo := Process.filterDocInfo module.members
-    for decl in declInfo do
-      jsonDecls := (← DocInfo.toJson module.name decl) :: jsonDecls
-      if let .instanceInfo i := decl then
-        instances := instances.push {
-          name := i.name.toString,
-          className := i.className.toString
-          typeNames := i.typeNames.map Name.toString
-        }
-    let jsonMod : JsonModule :=  {
-      name := module.name.toString,
-      declarations := jsonDecls,
-      instances,
-      imports := module.imports.map Name.toString
-    }
-    return ToJson.toJson jsonMod
-
-end DocGen4.Output

DocGen4/Process.lean

@@ -1,21 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-
-import DocGen4.Process.Analyze
-import DocGen4.Process.Attributes
-import DocGen4.Process.AxiomInfo
-import DocGen4.Process.Base
-import DocGen4.Process.ClassInfo
-import DocGen4.Process.DefinitionInfo
-import DocGen4.Process.DocInfo
-import DocGen4.Process.Hierarchy
-import DocGen4.Process.InductiveInfo
-import DocGen4.Process.InstanceInfo
-import DocGen4.Process.NameExt
-import DocGen4.Process.NameInfo
-import DocGen4.Process.OpaqueInfo
-import DocGen4.Process.StructureInfo
-import DocGen4.Process.TheoremInfo

DocGen4/Process/Analyze.lean

@@ -1,158 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-
-import Lean
-import Lean.Data.HashMap
-import Lean.Data.HashSet
-
-import DocGen4.Process.Base
-import DocGen4.Process.Hierarchy
-import DocGen4.Process.DocInfo
-
-namespace DocGen4.Process
-
-open Lean Meta
-
-/--
-Member of a module, either a declaration or some module doc string.
--/
-inductive ModuleMember where
-| docInfo (info : DocInfo) : ModuleMember
-| modDoc (doc : ModuleDoc) : ModuleMember
-deriving Inhabited
-
-/--
-A Lean module.
--/
-structure Module where
-  /--
-  Name of the module.
-  -/
-  name : Name
-  /--
-  All members of the module, sorted according to their line numbers.
-  -/
-  members : Array ModuleMember
-  imports : Array Name
-  deriving Inhabited
-
-/--
-The result of running a full doc-gen analysis on a project.
--/
-structure AnalyzerResult where
-  /--
-  The map from module names to indices of the `moduleNames` array.
-  -/
-  name2ModIdx : HashMap Name ModuleIdx
-  /--
-  The list of all modules, accessible nicely via `name2ModIdx`.
-  -/
-  moduleNames : Array Name
-  /--
-  A map from module names to information about these modules.
-  -/
-  moduleInfo : HashMap Name Module
-  deriving Inhabited
-
-namespace ModuleMember
-
-def getDeclarationRange : ModuleMember → DeclarationRange
-| docInfo i => i.getDeclarationRange
-| modDoc i => i.declarationRange
-
-/--
-An order for module members, based on their declaration range.
--/
-def order (l r : ModuleMember) : Bool :=
-  Position.lt l.getDeclarationRange.pos r.getDeclarationRange.pos
-
-def getName : ModuleMember → Name
-| docInfo i => i.getName
-| modDoc _ => Name.anonymous
-
-def getDocString : ModuleMember → Option String
-| docInfo i => i.getDocString
-| modDoc i => i.doc
-
-def shouldRender : ModuleMember → Bool
-| docInfo i => i.shouldRender
-| modDoc _ => true
-
-end ModuleMember
-
-inductive AnalyzeTask where
-| loadAll (load : List Name) : AnalyzeTask
-| loadAllLimitAnalysis (analyze : List Name) : AnalyzeTask
-
-def AnalyzeTask.getLoad : AnalyzeTask → List Name
-| loadAll load => load
-| loadAllLimitAnalysis load => load
-
-def getAllModuleDocs (relevantModules : Array Name) : MetaM (HashMap Name Module) := do
-  let env ← getEnv
-  let mut res := mkHashMap relevantModules.size
-  for module in relevantModules do
-    let modDocs := getModuleDoc? env module |>.getD #[] |>.map .modDoc
-    let some modIdx := env.getModuleIdx? module | unreachable!
-    let moduleData := env.header.moduleData.get! modIdx
-    let imports := moduleData.imports.map Import.module
-    res := res.insert module <| Module.mk module modDocs imports
-  return res
-
-/--
-Run the doc-gen analysis on all modules that are loaded into the `Environment`
-of this `MetaM` run and mentioned by the `AnalyzeTask`.
--/
-def process (task : AnalyzeTask) : MetaM (AnalyzerResult × Hierarchy) := do
-  let env ← getEnv
-  let relevantModules := match task with
-    | .loadAll _ => HashSet.fromArray env.header.moduleNames
-    | .loadAllLimitAnalysis analysis => HashSet.fromArray analysis.toArray
-  let allModules := env.header.moduleNames
-
-  let mut res ← getAllModuleDocs relevantModules.toArray
-
-  for (name, cinfo) in env.constants.toList do
-    let some modidx := env.getModuleIdxFor? name | unreachable!
-    let moduleName := env.allImportedModuleNames.get! modidx
-    if !relevantModules.contains moduleName then
-      continue
-
-    try
-      let config := {
-        maxHeartbeats := 5000000,
-        options := ← getOptions,
-        fileName := ← getFileName,
-        fileMap := ← getFileMap
-      }
-      let analysis ← Prod.fst <$> Meta.MetaM.toIO (DocInfo.ofConstant (name, cinfo)) config { env := env } {} {}
-      if let some dinfo := analysis then
-        let moduleName := env.allImportedModuleNames.get! modidx
-        let module := res.find! moduleName
-        res := res.insert moduleName {module with members := module.members.push (ModuleMember.docInfo dinfo)}
-    catch e =>
-      IO.println s!"WARNING: Failed to obtain information for: {name}: {← e.toMessageData.toString}"
-
-  -- TODO: This could probably be faster if we did sorted insert above instead
-  for (moduleName, module) in res.toArray do
-    res := res.insert moduleName {module with members := module.members.qsort ModuleMember.order}
-
-  let hierarchy := Hierarchy.fromArray allModules
-  let analysis := {
-    name2ModIdx := env.const2ModIdx,
-    moduleNames := allModules,
-    moduleInfo := res,
-  }
-  return (analysis, hierarchy)
-
-def filterDocInfo (ms : Array ModuleMember) : Array DocInfo :=
-  ms.filterMap filter
-  where
-    filter : ModuleMember → Option DocInfo
-    | ModuleMember.docInfo i => some i
-    | _ => none
-
-end DocGen4.Process

DocGen4/Process/Attributes.lean

@@ -1,174 +0,0 @@
-import Lean
-
-namespace DocGen4
-
-open Lean Meta
--- The following is probably completely overengineered but I love it
-
-/--
-Captures the notion of a value based attributes, `attrKind` is things like
-`EnumAttributes`.
--/
-class ValueAttr (attrKind : Type → Type) where
-  /--
-  Given a certain value based attribute, an `Environment` and the `Name` of
-  a declaration returns the value of the attribute on this declaration if present.
-  -/
-  getValue {α : Type} [Inhabited α] [ToString α] : attrKind α → Environment → Name → Option String
-
-/--
-Contains a specific attribute declaration of a certain attribute kind (enum based, parametric etc.).
--/
-structure ValueAttrWrapper (attrKind : Type → Type) [ValueAttr attrKind] where
-  {α : Type}
-  attr : attrKind α
-  [str : ToString α]
-  [inhab : Inhabited α]
-
-/--
-Obtain the value of an enum attribute for a certain name.
--/
-def enumGetValue {α : Type} [Inhabited α] [ToString α] (attr : EnumAttributes α) (env : Environment) (decl : Name) : Option String := do
-  let val ← EnumAttributes.getValue attr env decl
-  some (toString val)
-
-instance : ValueAttr EnumAttributes where
-  getValue := enumGetValue
-
-/--
-Obtain the value of a parametric attribute for a certain name.
--/
-def parametricGetValue {α : Type} [Inhabited α] [ToString α] (attr : ParametricAttribute α) (env : Environment) (decl : Name) : Option String := do
-  let val ← ParametricAttribute.getParam? attr env decl
-  some (attr.attr.name.toString ++ " " ++ toString val)
-
-instance : ValueAttr ParametricAttribute where
-  getValue := parametricGetValue
-
-abbrev EnumAttrWrapper := ValueAttrWrapper EnumAttributes
-abbrev ParametricAttrWrapper := ValueAttrWrapper ParametricAttribute
-
-/--
-The list of all tag based attributes doc-gen knows about and can recover.
--/
-def tagAttributes : Array TagAttribute :=
-  #[IR.UnboxResult.unboxAttr, neverExtractAttr,
-    Elab.Term.elabWithoutExpectedTypeAttr, matchPatternAttr]
-
-deriving instance Repr for Compiler.InlineAttributeKind
-deriving instance Repr for Compiler.SpecializeAttributeKind
-
-open Compiler in
-instance : ToString InlineAttributeKind where
-  toString kind :=
-    match kind with
-    | .inline => "inline"
-    | .noinline => "noinline"
-    | .macroInline => "macro_inline"
-    | .inlineIfReduce => "inline_if_reduce"
-    | .alwaysInline => "always_inline"
-
-open Compiler in
-instance : ToString SpecializeAttributeKind where
-  toString kind :=
-    match kind with
-    | .specialize => "specialize"
-    | .nospecialize => "nospecialize"
-
-instance : ToString ReducibilityStatus where
-  toString kind :=
-    match kind with
-    | .reducible => "reducible"
-    | .semireducible => "semireducible"
-    | .irreducible => "irreducible"
-
-/--
-The list of all enum based attributes doc-gen knows about and can recover.
--/
-@[reducible]
-def enumAttributes : Array EnumAttrWrapper := #[⟨Compiler.inlineAttrs⟩, ⟨reducibilityAttrs⟩]
-
-instance : ToString ExternEntry where
-  toString entry :=
-    match entry with
-    | .adhoc `all => ""
-    | .adhoc backend => s!"{backend} adhoc"
-    | .standard `all fn => fn
-    | .standard backend fn => s!"{backend} {fn}"
-    | .inline backend pattern => s!"{backend} inline {String.quote pattern}"
-    -- TODO: The docs in the module dont specific how to render this
-    | .foreign backend fn  => s!"{backend} foreign {fn}"
-
-instance : ToString ExternAttrData where
-  toString data := (data.arity?.map toString |>.getD "") ++ " " ++ String.intercalate " " (data.entries.map toString)
-
-/--
-The list of all parametric attributes (that is, attributes with any kind of information attached)
-doc-gen knows about and can recover.
--/
-def parametricAttributes : Array ParametricAttrWrapper := #[⟨externAttr⟩, ⟨Compiler.implementedByAttr⟩, ⟨exportAttr⟩, ⟨Compiler.specializeAttr⟩]
-
-def getTags (decl : Name) : MetaM (Array String) := do
-  let env ← getEnv
-  return tagAttributes.filter (TagAttribute.hasTag · env decl) |>.map (·.attr.name.toString)
-
-def getValuesAux {α : Type} {attrKind : Type → Type} [va : ValueAttr attrKind] [Inhabited α] [ToString α] (decl : Name) (attr : attrKind α) : MetaM (Option String) := do
-  let env ← getEnv
-  return va.getValue attr env decl
-
-def getValues {attrKind : Type → Type} [ValueAttr attrKind] (decl : Name) (attrs : Array (ValueAttrWrapper attrKind)) : MetaM (Array String) := do
-  let mut res := #[]
-  for attr in attrs do
-    if let some val ← @getValuesAux attr.α attrKind _ attr.inhab attr.str decl attr.attr then
-      res := res.push val
-  return res
-
-def getEnumValues (decl : Name) : MetaM (Array String) := getValues decl enumAttributes
-def getParametricValues (decl : Name) : MetaM (Array String) := getValues decl parametricAttributes
-
-def getDefaultInstance (decl : Name) (className : Name) : MetaM (Option String) := do
-  let insts ← getDefaultInstances className
-  for (inst, prio) in insts do
-    if inst == decl then
-      return some s!"defaultInstance {prio}"
-  return none
-
-def hasSimp (decl : Name) : MetaM (Option String) := do
-  let thms ← simpExtension.getTheorems
-  if thms.isLemma (.decl decl) then
-    return "simp"
-  else
-    return none
-
-def hasCsimp (decl : Name) : MetaM (Option String) := do
-  let env ← getEnv
-  if Compiler.hasCSimpAttribute env decl then
-    return some "csimp"
-  else
-    return none
-
-/--
-The list of custom attributes, that don't fit in the parametric or enum
-attribute kinds, doc-gen konws about and can recover.
--/
-def customAttrs := #[hasSimp, hasCsimp]
-
-def getCustomAttrs (decl : Name) : MetaM (Array String) := do
-  let mut values := #[]
-  for attr in customAttrs do
-    if let some value ← attr decl then
-      values := values.push value
-  return values
-
-/--
-The main entry point for recovering all attribute values for a given
-declaration.
--/
-def getAllAttributes (decl : Name) : MetaM (Array String) := do
-  let tags ← getTags decl
-  let enums ← getEnumValues decl
-  let parametric ← getParametricValues decl
-  let customs ← getCustomAttrs decl
-  return customs ++ tags ++ enums ++ parametric
-
-end DocGen4

DocGen4/Process/AxiomInfo.lean

@@ -1,22 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-
-namespace DocGen4.Process
-
-open Lean Meta
-
-def AxiomInfo.ofAxiomVal (v : AxiomVal) : MetaM AxiomInfo := do
-  let info ← Info.ofConstantVal v.toConstantVal
-  return {
-    toInfo := info,
-    isUnsafe := v.isUnsafe
-  } 
-
-end DocGen4.Process

DocGen4/Process/Base.lean

@@ -1,196 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-
-import Lean
-
-namespace DocGen4.Process
-open Lean Widget Meta
-
-/--
-Stores information about a typed name.
--/
-structure NameInfo where
-  /--
-  The name that has this info attached.
-  -/
-  name  : Name
-  /--
-  The pretty printed type of this name.
-  -/
-  type : CodeWithInfos
-  /--
-  The doc string of the name if it exists.
-  -/
-  doc : Option String
-  deriving Inhabited
-
-/--
-An argument to a declaration, e.g. the `(x : Nat)` in `def foo (x : Nat) := x`.
--/
-structure Arg where
-  /--
-  The name of the argument.
-  -/
-  name : Name
-  /--
-  The pretty printed type of the argument.
-  -/
-  type : CodeWithInfos
-  /--
-  What kind of binder was used for the argument.
-  -/
-  binderInfo : BinderInfo
-
-/--
-A base structure for information about a declaration.
--/
-structure Info extends NameInfo where
-  /--
-  The list of arguments to the declaration.
-  -/
-  args : Array Arg
-  /--
-  In which lines the declaration was created.
-  -/
-  declarationRange : DeclarationRange
-  /--
-  A list of (known) attributes that are attached to the declaration.
-  -/
-  attrs : Array String
-  /--
-  Whether this info item should be rendered
-  -/
-  render : Bool := true
-  deriving Inhabited
-
-/--
-Information about an `axiom` declaration.
--/
-structure AxiomInfo extends Info where
-  isUnsafe : Bool
-  deriving Inhabited
-
-/--
-Information about a `theorem` declaration.
--/
-structure TheoremInfo extends Info
-  deriving Inhabited
-
-/--
-Information about an `opaque` declaration.
--/
-structure OpaqueInfo extends Info where
-  /--
-  The pretty printed value of the declaration.
-  -/
-  value : CodeWithInfos
-  /--
-  A value of partial is interpreted as this opaque being part of a partial def
-  since the actual definition for a partial def is hidden behind an inaccessible value.
-  -/
-  definitionSafety : DefinitionSafety
-  deriving Inhabited
-
-/--
-Information about a `def` declaration, note that partial defs are handled by `OpaqueInfo`.
--/
-structure DefinitionInfo extends Info where
-  isUnsafe : Bool
-  hints : ReducibilityHints
-  equations : Option (Array CodeWithInfos)
-  isNonComputable : Bool
-  deriving Inhabited
-
-/--
-Information about an `instance` declaration.
--/
-structure InstanceInfo extends DefinitionInfo where
-  className : Name
-  typeNames : Array Name
-  deriving Inhabited
-
-/--
-Information about an `inductive` declaration
--/
-structure InductiveInfo extends Info where
-  /--
-  List of all constructors of this inductive type.
-  -/
-  ctors : List NameInfo
-  isUnsafe : Bool
-  deriving Inhabited
-
-/--
-Information about a `structure` declaration.
--/
-structure StructureInfo extends Info where
-  /--
-  Information about all the fields of the structure.
-  -/
-  fieldInfo : Array NameInfo
-  /--
-  All the structures this one inherited from.
-  -/
-  parents : Array Name
-  /--
-  The constructor of the structure.
-  -/
-  ctor : NameInfo
-  deriving Inhabited
-
-/--
-Information about a `class` declaration.
--/
-abbrev ClassInfo := StructureInfo
-
-/--
-Information about a `class inductive` declaration.
--/
-abbrev ClassInductiveInfo := InductiveInfo
-
-
-/--
-Information about a constructor of an inductive type
--/
-abbrev ConstructorInfo := Info
-
-/--
-A general type for informations about declarations.
--/
-inductive DocInfo where
-| axiomInfo (info : AxiomInfo) : DocInfo
-| theoremInfo (info : TheoremInfo) : DocInfo
-| opaqueInfo (info : OpaqueInfo) : DocInfo
-| definitionInfo (info : DefinitionInfo) : DocInfo
-| instanceInfo (info : InstanceInfo) : DocInfo
-| inductiveInfo (info : InductiveInfo) : DocInfo
-| structureInfo (info : StructureInfo) : DocInfo
-| classInfo (info : ClassInfo) : DocInfo
-| classInductiveInfo (info : ClassInductiveInfo) : DocInfo
-| ctorInfo (info : ConstructorInfo) : DocInfo
-  deriving Inhabited
-
-/--
-Turns an `Expr` into a pretty printed `CodeWithInfos`.
--/
-def prettyPrintTerm (expr : Expr) : MetaM CodeWithInfos := do
-  let ⟨fmt, infos⟩ ← PrettyPrinter.ppExprWithInfos expr
-  let tt := TaggedText.prettyTagged fmt
-  let ctx := {
-    env := ← getEnv
-    mctx := ← getMCtx
-    options := ← getOptions
-    currNamespace := ← getCurrNamespace
-    openDecls := ← getOpenDecls
-    fileMap := default,
-    ngen := ← getNGen
-  }
-  return tagCodeInfos ctx infos tt
-
-def isInstance (declName : Name) : MetaM Bool := do
-  return (instanceExtension.getState (← getEnv)).instanceNames.contains declName
-
-end DocGen4.Process

DocGen4/Process/ClassInfo.lean

@@ -1,24 +0,0 @@
-
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-import DocGen4.Process.StructureInfo
-import DocGen4.Process.InductiveInfo
-
-namespace DocGen4.Process
-
-open Lean Meta 
-
-def ClassInfo.ofInductiveVal (v : InductiveVal) : MetaM ClassInfo := do
-  StructureInfo.ofInductiveVal v
-
-def ClassInductiveInfo.ofInductiveVal (v : InductiveVal) : MetaM ClassInductiveInfo := do
-  InductiveInfo.ofInductiveVal v
-
-end DocGen4.Process

DocGen4/Process/DefinitionInfo.lean

@@ -1,75 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-
-namespace DocGen4.Process
-
-open Lean Meta Widget
-
-partial def stripArgs (e : Expr) : Expr :=
-  match e.consumeMData with
-  | Expr.lam name _ body _ =>
-    let name := name.eraseMacroScopes
-    stripArgs (Expr.instantiate1 body (mkFVar ⟨name⟩))
-  | Expr.forallE name _ body _ =>
-    let name := name.eraseMacroScopes
-    stripArgs (Expr.instantiate1 body (mkFVar ⟨name⟩))
-  | _ => e
-
-def processEq (eq : Name) : MetaM CodeWithInfos := do
-  let type ← (mkConstWithFreshMVarLevels eq >>= inferType)
-  let final := stripArgs type
-  prettyPrintTerm final
-
-def valueToEq (v : DefinitionVal) : MetaM Expr := withLCtx {} {} do
-  withOptions (tactic.hygienic.set . false) do
-    lambdaTelescope v.value fun xs body => do
-      let us := v.levelParams.map mkLevelParam
-      let type ← mkEq (mkAppN (Lean.mkConst v.name us) xs) body
-      let type ← mkForallFVars xs type
-      return type
-
-def DefinitionInfo.ofDefinitionVal (v : DefinitionVal) : MetaM DefinitionInfo := do
-  let info ← Info.ofConstantVal v.toConstantVal
-  let isUnsafe := v.safety == DefinitionSafety.unsafe
-  let isNonComputable := isNoncomputable (← getEnv) v.name
-  try
-    let eqs? ← getEqnsFor? v.name
-    match eqs? with
-    | some eqs =>
-      let equations ← eqs.mapM processEq
-      return {
-        toInfo := info,
-        isUnsafe,
-        hints := v.hints,
-        equations,
-        isNonComputable
-      }
-    | none =>
-      let equations := #[← prettyPrintTerm <| stripArgs (← valueToEq v)]
-      return {
-        toInfo := info,
-        isUnsafe,
-        hints := v.hints,
-        equations,
-        isNonComputable
-      }
-  catch err =>
-    IO.println s!"WARNING: Failed to calculate equational lemmata for {v.name}: {← err.toMessageData.toString}"
-    return {
-      toInfo := info,
-      isUnsafe,
-      hints := v.hints,
-      equations := none,
-      isNonComputable
-    }
-
-
-
-end DocGen4.Process

DocGen4/Process/DocInfo.lean

@@ -1,223 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.AxiomInfo
-import DocGen4.Process.TheoremInfo
-import DocGen4.Process.OpaqueInfo
-import DocGen4.Process.InstanceInfo
-import DocGen4.Process.DefinitionInfo
-import DocGen4.Process.ClassInfo
-import DocGen4.Process.StructureInfo
-import DocGen4.Process.InductiveInfo
-
-
-namespace DocGen4.Process
-namespace DocInfo
-
-open Lean Meta Widget
-
-def getDeclarationRange : DocInfo → DeclarationRange
-| axiomInfo i => i.declarationRange
-| theoremInfo i => i.declarationRange
-| opaqueInfo i => i.declarationRange
-| definitionInfo i => i.declarationRange
-| instanceInfo i => i.declarationRange
-| inductiveInfo i => i.declarationRange
-| structureInfo i => i.declarationRange
-| classInfo i => i.declarationRange
-| classInductiveInfo i => i.declarationRange
-| ctorInfo i => i.declarationRange
-
-def getName : DocInfo → Name
-| axiomInfo i => i.name
-| theoremInfo i => i.name
-| opaqueInfo i => i.name
-| definitionInfo i => i.name
-| instanceInfo i => i.name
-| inductiveInfo i => i.name
-| structureInfo i => i.name
-| classInfo i => i.name
-| classInductiveInfo i => i.name
-| ctorInfo i => i.name
-
-def getKind : DocInfo → String
-| axiomInfo _ => "axiom"
-| theoremInfo _ => "theorem"
-| opaqueInfo _ => "opaque"
-| definitionInfo _ => "def"
-| instanceInfo _ => "instance"
-| inductiveInfo _ => "inductive"
-| structureInfo _ => "structure"
-| classInfo _ => "class"
-| classInductiveInfo _ => "class"
-| ctorInfo _ => "ctor" -- TODO: kind ctor support in js
-
-def getType : DocInfo → CodeWithInfos
-| axiomInfo i => i.type
-| theoremInfo i => i.type
-| opaqueInfo i => i.type
-| definitionInfo i => i.type
-| instanceInfo i => i.type
-| inductiveInfo i => i.type
-| structureInfo i => i.type
-| classInfo i => i.type
-| classInductiveInfo i => i.type
-| ctorInfo i => i.type
-
-def getArgs : DocInfo → Array Arg
-| axiomInfo i => i.args
-| theoremInfo i => i.args
-| opaqueInfo i => i.args
-| definitionInfo i => i.args
-| instanceInfo i => i.args
-| inductiveInfo i => i.args
-| structureInfo i => i.args
-| classInfo i => i.args
-| classInductiveInfo i => i.args
-| ctorInfo i => i.args
-
-def getAttrs : DocInfo → Array String
-| axiomInfo i => i.attrs
-| theoremInfo i => i.attrs
-| opaqueInfo i => i.attrs
-| definitionInfo i => i.attrs
-| instanceInfo i => i.attrs
-| inductiveInfo i => i.attrs
-| structureInfo i => i.attrs
-| classInfo i => i.attrs
-| classInductiveInfo i => i.attrs
-| ctorInfo i => i.attrs
-
-def getDocString : DocInfo → Option String
-| axiomInfo i => i.doc
-| theoremInfo i => i.doc
-| opaqueInfo i => i.doc
-| definitionInfo i => i.doc
-| instanceInfo i => i.doc
-| inductiveInfo i => i.doc
-| structureInfo i => i.doc
-| classInfo i => i.doc
-| classInductiveInfo i => i.doc
-| ctorInfo i => i.doc
-
-def shouldRender : DocInfo → Bool
-| axiomInfo i => i.render
-| theoremInfo i => i.render
-| opaqueInfo i => i.render
-| definitionInfo i => i.render
-| instanceInfo i => i.render
-| inductiveInfo i => i.render
-| structureInfo i => i.render
-| classInfo i => i.render
-| classInductiveInfo i => i.render
-| ctorInfo i => i.render
-
-def isBlackListed (declName : Name) : MetaM Bool := do
-  match ← findDeclarationRanges? declName with
-  | some _ =>
-    let env ← getEnv
-    pure (declName.isInternal)
-    <||> (pure <| isAuxRecursor env declName)
-    <||> (pure <| isNoConfusion env declName)
-    <||> isRec declName
-    <||> isMatcher declName
-  -- TODO: Evaluate whether filtering out declarations without range is sensible
-  | none => return true
-
--- TODO: Is this actually the best way?
-def isProjFn (declName : Name) : MetaM Bool := do
-  let env ← getEnv
-  match declName with
-  | Name.str parent name =>
-    if isStructure env parent then
-      match getStructureInfo? env parent with
-      | some i =>
-        match i.fieldNames.find? (· == name) with
-        | some _ => return true
-        | none => return false
-      | none => panic! s!"{parent} is not a structure"
-    else
-      return false
-  | _ => return false
-
-def ofConstant : (Name × ConstantInfo) → MetaM (Option DocInfo) := fun (name, info) => do
-  if ← isBlackListed name then
-    return none
-  match info with
-  | ConstantInfo.axiomInfo i => return some <| axiomInfo (← AxiomInfo.ofAxiomVal i)
-  | ConstantInfo.thmInfo i => return some <| theoremInfo (← TheoremInfo.ofTheoremVal i)
-  | ConstantInfo.opaqueInfo i => return some <| opaqueInfo (← OpaqueInfo.ofOpaqueVal i)
-  | ConstantInfo.defnInfo i =>
-    if ← isProjFn i.name then
-      let info ← DefinitionInfo.ofDefinitionVal i
-      return some <| definitionInfo { info with render := false }
-    else
-      if ← isInstance i.name then
-        let info ← InstanceInfo.ofDefinitionVal i
-        return some <| instanceInfo info
-      else
-        let info ← DefinitionInfo.ofDefinitionVal i
-        return some <| definitionInfo  info
-  | ConstantInfo.inductInfo i =>
-    let env ← getEnv
-    if isStructure env i.name then
-      if isClass env i.name then
-        return some <| classInfo (← ClassInfo.ofInductiveVal i)
-      else
-        return some <| structureInfo (← StructureInfo.ofInductiveVal i)
-    else
-      if isClass env i.name then
-        return some <| classInductiveInfo (← ClassInductiveInfo.ofInductiveVal i)
-      else
-        return some <| inductiveInfo (← InductiveInfo.ofInductiveVal i)
-  | ConstantInfo.ctorInfo i =>
-    let info ← Info.ofConstantVal i.toConstantVal
-    return some <| ctorInfo { info with render := false }
-  -- we ignore these for now
-  | ConstantInfo.recInfo _ | ConstantInfo.quotInfo _ => return none
-
-def getKindDescription : DocInfo → String
-| axiomInfo i => if i.isUnsafe then "unsafe axiom" else "axiom"
-| theoremInfo _ => "theorem"
-| opaqueInfo i =>
-  match i.definitionSafety with
-  | DefinitionSafety.safe => "opaque"
-  | DefinitionSafety.unsafe => "unsafe opaque"
-  | DefinitionSafety.partial => "partial def"
-| definitionInfo i => Id.run do
-  let mut modifiers := #[]
-  if i.isUnsafe then
-    modifiers := modifiers.push "unsafe"
-  if i.isNonComputable then
-    modifiers := modifiers.push "noncomputable"
-
-  let defKind :=
-    if i.hints.isAbbrev then
-      "abbrev"
-    else
-      "def"
-  modifiers := modifiers.push defKind
-  return String.intercalate " " modifiers.toList
-| instanceInfo i => Id.run do
-  let mut modifiers := #[]
-  if i.isUnsafe then
-    modifiers := modifiers.push "unsafe"
-  if i.isNonComputable then
-    modifiers := modifiers.push "noncomputable"
-
-  modifiers := modifiers.push "instance"
-  return String.intercalate " " modifiers.toList
-| inductiveInfo i => if i.isUnsafe then "unsafe inductive" else "inductive"
-| structureInfo _ => "structure"
-| classInfo _ => "class"
-| classInductiveInfo _ => "class inductive"
-| ctorInfo _ => "constructor"
-
-end DocInfo
-
-end DocGen4.Process

DocGen4/Process/Hierarchy.lean

@@ -1,136 +0,0 @@
-/-
-Copyright (c) 2021 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-import Lean.Data.HashMap
-
-import DocGen4.Process.NameExt
-
-def Lean.HashSet.fromArray [BEq α] [Hashable α] (xs : Array α) : Lean.HashSet α :=
-  xs.foldr (flip .insert) .empty
-
-namespace DocGen4
-
-open Lean Name
-
-def getNLevels (name : Name) (levels: Nat) : Name :=
-  let components := name.componentsRev
-  (components.drop (components.length - levels)).reverse.foldl (· ++ ·) Name.anonymous
-
-inductive Hierarchy where
-| node (name : NameExt) (isFile : Bool) (children : RBNode NameExt (fun _ => Hierarchy)) : Hierarchy
-
-instance : Inhabited Hierarchy := ⟨Hierarchy.node ⟨.anonymous, .html⟩ false RBNode.leaf⟩
-
-abbrev HierarchyMap := RBNode NameExt (fun _ => Hierarchy)
-
--- Everything in this namespace is adapted from stdlib's RBNode
-namespace HierarchyMap
-
-def toList : HierarchyMap → List (NameExt × Hierarchy)
-| t => t.revFold (fun ps k v => (k, v)::ps) []
-
-def toArray : HierarchyMap → Array (NameExt × Hierarchy)
-| t => t.fold (fun ps k v => ps ++ #[(k, v)] ) #[]
-
-def hForIn [Monad m] (t : HierarchyMap) (init : σ) (f : (NameExt × Hierarchy) → σ → m (ForInStep σ)) : m σ :=
-  t.forIn init (fun a b acc => f (a, b) acc)
-
-instance : ForIn m HierarchyMap (NameExt × Hierarchy) where
-  forIn := HierarchyMap.hForIn
-
-end HierarchyMap
-
-namespace Hierarchy
-
-def empty (n : NameExt) (isFile : Bool) : Hierarchy :=
-  node n isFile RBNode.leaf
-
-def getName : Hierarchy → Name
-| node n _ _ => n.name
-
-def getNameExt : Hierarchy → NameExt
-| node n _ _ => n
-
-def getChildren : Hierarchy → HierarchyMap
-| node _ _ c => c
-
-def isFile : Hierarchy → Bool
-| node _ f _ => f
-
-partial def insert! (h : Hierarchy) (n : NameExt) : Hierarchy := Id.run do
-  let hn := h.getNameExt
-  let mut cs := h.getChildren
-
-  if getNumParts hn.name + 1 == getNumParts n.name then
-    match cs.find NameExt.cmp n with
-    | none =>
-      node hn h.isFile (cs.insert NameExt.cmp n <| empty n true)
-    | some (node _ true _) => h
-    | some (node _ false ccs) =>
-        cs := cs.erase NameExt.cmp n
-        node hn h.isFile (cs.insert NameExt.cmp n <| node n true ccs)
-  else
-    let leveled := ⟨getNLevels n.name (getNumParts hn.name + 1), .html⟩
-    match cs.find NameExt.cmp leveled with
-    | some nextLevel =>
-      cs := cs.erase NameExt.cmp leveled
-      -- BUG?
-      node hn h.isFile <| cs.insert NameExt.cmp leveled (nextLevel.insert! n)
-    | none =>
-      let child := (insert! (empty leveled false) n)
-      node hn h.isFile <| cs.insert NameExt.cmp leveled child
-
-partial def fromArray (names : Array Name) : Hierarchy :=
-   (names.map (fun n => NameExt.mk n .html)).foldl insert! (empty ⟨anonymous, .html⟩ false)
-
-partial def fromArrayExt (names : Array NameExt) : Hierarchy :=
-  names.foldl insert! (empty ⟨anonymous, .html⟩ false)
-
-def baseDirBlackList : HashSet String :=
-  HashSet.fromArray #[
-    "404.html",
-    "color-scheme.js",
-    "declaration-data.js",
-    "declarations",
-    "find",
-    "how-about.js",
-    "index.html",
-    "search.html",
-    "foundational_types.html",
-    "mathjax-config.js",
-    "navbar.html",
-    "nav.js",
-    "search.js",
-    "src",
-    "style.css"
-  ]
-
-partial def fromDirectoryAux (dir : System.FilePath) (previous : Name) : IO (Array NameExt) := do
-  let mut children := #[]
-  for entry in ← System.FilePath.readDir dir do
-    if ← entry.path.isDir then
-      children := children ++ (← fromDirectoryAux entry.path (.str previous entry.fileName))
-    else if entry.path.extension = some "html" then
-      children := children.push <| ⟨.str previous (entry.fileName.dropRight ".html".length), .html⟩
-    else if entry.path.extension = some "pdf" then
-      children := children.push <| ⟨.str previous (entry.fileName.dropRight ".pdf".length), .pdf⟩
-  return children
-
-def fromDirectory (dir : System.FilePath) : IO Hierarchy := do
-    let mut children := #[]
-    for entry in ← System.FilePath.readDir dir do
-      if baseDirBlackList.contains entry.fileName then
-        continue
-      else if ← entry.path.isDir then
-        children := children ++ (← fromDirectoryAux entry.path (.mkSimple entry.fileName))
-      else if entry.path.extension = some "html" then
-        children := children.push <| ⟨.mkSimple (entry.fileName.dropRight ".html".length), .html⟩
-      else if entry.path.extension = some "pdf" then
-        children := children.push <| ⟨.mkSimple (entry.fileName.dropRight ".pdf".length), .pdf⟩
-    return Hierarchy.fromArrayExt children
-
-end Hierarchy
-end DocGen4

DocGen4/Process/InductiveInfo.lean

@@ -1,30 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-
-namespace DocGen4.Process
-
-open Lean Meta 
-
-def getConstructorType (ctor : Name) : MetaM Expr := do
-  let env ← getEnv
-  match env.find? ctor with
-  | some (ConstantInfo.ctorInfo i) => pure i.type
-  | _ => panic! s!"Constructor {ctor} was requested but does not exist"
-
-def InductiveInfo.ofInductiveVal (v : InductiveVal) : MetaM InductiveInfo := do
-  let info ← Info.ofConstantVal v.toConstantVal
-  let ctors ← v.ctors.mapM (fun name => do NameInfo.ofTypedName name (← getConstructorType name))
-  return {
-    toInfo := info,
-    ctors,
-    isUnsafe := v.isUnsafe
-  }
-
-end DocGen4.Process

DocGen4/Process/InstanceInfo.lean

@@ -1,41 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-import DocGen4.Process.DefinitionInfo
-
-namespace DocGen4.Process
-
-open Lean Meta
-
-def getInstanceTypes (typ : Expr) : MetaM (Array Name) := do
-  let (_, _, tail) ← forallMetaTelescopeReducing typ
-  let args := tail.getAppArgs
-  let (_, names) ← args.mapM (Expr.forEach · findName) |>.run .empty
-  return names
-where
-  findName : Expr → StateRefT (Array Name) MetaM Unit
-    | .const name _ => modify (·.push name)
-    | .sort .zero => modify (·.push "_builtin_prop")
-    | .sort (.succ _) => modify (·.push "_builtin_typeu")
-    | .sort _ => modify (·.push "_builtin_sortu")
-    | _ => return ()
-
-def InstanceInfo.ofDefinitionVal (v : DefinitionVal) : MetaM InstanceInfo := do
-  let mut info ← DefinitionInfo.ofDefinitionVal v
-  let some className ← isClass? v.type | unreachable!
-  if let some instAttr ← getDefaultInstance v.name className then
-    info := { info with attrs := info.attrs.push instAttr }
-  let typeNames ← getInstanceTypes v.type
-  return {
-    toDefinitionInfo := info,
-    className,
-    typeNames
-  }
-
-end DocGen4.Process

DocGen4/Process/NameExt.lean

@@ -1,48 +0,0 @@
-/-
-A generalization of `Lean.Name` that includes a file extension.
--/
-import Lean
-
-open Lean Name
-
-inductive Extension where
-| html
-| pdf
-deriving Repr
-
-namespace Extension
-
-def cmp : Extension → Extension → Ordering
-  | html, html => Ordering.eq
-  | html, _ => Ordering.lt
-  | pdf, pdf => Ordering.eq
-  | pdf, _ => Ordering.gt
-
-instance : BEq Extension where
-  beq e1 e2 :=
-    match cmp e1 e2 with
-    | Ordering.eq => true
-    | _ => false
-
-def toString : Extension → String
-  | html => "html"
-  | pdf => "pdf"
-
-end Extension
-
-structure NameExt where
-  name : Name
-  ext : Extension
-
-namespace NameExt
-
-def cmp (n₁ n₂ : NameExt) : Ordering :=
-  match Name.cmp n₁.name n₂.name with
-  | Ordering.eq => Extension.cmp n₁.ext n₂.ext
-  | ord => ord
-
-def getString! : NameExt → String
-  | ⟨str _ s, _⟩ => s
-  | _       => unreachable!
-
-end NameExt

DocGen4/Process/NameInfo.lean

@@ -1,50 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.Attributes
-
-namespace DocGen4.Process
-open Lean Meta
-
-def NameInfo.ofTypedName (n : Name) (t : Expr) : MetaM NameInfo := do
-  let env ← getEnv
-  return { name := n, type := ← prettyPrintTerm t, doc := ← findDocString? env n}
-
-partial def typeToArgsType (e : Expr) : (Array (Name × Expr × BinderInfo) × Expr) :=
-  let helper := fun name type body data =>
-    -- Once we hit a name with a macro scope we stop traversing the expression
-    -- and print what is left after the : instead. The only exception
-    -- to this is instances since these almost never have a name
-    -- but should still be printed as arguments instead of after the :.
-    if name.hasMacroScopes && !data.isInstImplicit then
-      (#[], e)
-    else
-      let name := name.eraseMacroScopes
-      let arg := (name, type, data)
-      let (args, final) := typeToArgsType (Expr.instantiate1 body (mkFVar ⟨name⟩))
-      (#[arg] ++ args, final)
-  match e.consumeMData with
-  | Expr.lam name type body binderInfo => helper name type body binderInfo
-  | Expr.forallE name type body binderInfo => helper name type body binderInfo
-  | _ => (#[], e)
-
-def Info.ofConstantVal (v : ConstantVal) : MetaM Info := do
-  let (args, type) := typeToArgsType v.type
-  let args ← args.mapM (fun (n, e, b) => do return Arg.mk n (← prettyPrintTerm e) b)
-  let nameInfo ← NameInfo.ofTypedName v.name type
-  match ← findDeclarationRanges? v.name with
-  -- TODO: Maybe selection range is more relevant? Figure this out in the future
-  | some range => return {
-      toNameInfo := nameInfo,
-      args,
-      declarationRange := range.range,
-      attrs := ← getAllAttributes v.name
-    }
-  | none => panic! s!"{v.name} is a declaration without position"
-
-end DocGen4.Process

DocGen4/Process/OpaqueInfo.lean

@@ -1,33 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-
-namespace DocGen4.Process
-
-open Lean Meta
-
-def OpaqueInfo.ofOpaqueVal (v : OpaqueVal) : MetaM OpaqueInfo := do
-  let info ← Info.ofConstantVal v.toConstantVal
-  let value ← prettyPrintTerm v.value
-  let env ← getEnv
-  let isPartial := env.find? (Compiler.mkUnsafeRecName v.name) |>.isSome
-  let definitionSafety :=
-    if isPartial then
-      DefinitionSafety.partial
-    else if v.isUnsafe then
-      DefinitionSafety.unsafe
-    else
-      DefinitionSafety.safe
-  return {
-    toInfo := info,
-    value,
-    definitionSafety
-  }
-
-end DocGen4.Process

DocGen4/Process/StructureInfo.lean

@@ -1,58 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-
-namespace DocGen4.Process
-
-open Lean Meta 
-
--- TODO: replace with Leos variant from Zulip
-def dropArgs (type : Expr) (n : Nat) : (Expr × List (Name × Expr)) :=
-  match type, n with
-  | e, 0 => (e, [])
-  | Expr.forallE name type body _, x + 1 =>
-    let body := body.instantiate1 <| mkFVar ⟨name⟩
-    let next := dropArgs body x
-    { next with snd := (name, type) :: next.snd}
-  | _, _ + 1 => panic! s!"No forallE left"
-
-def getFieldTypes (struct : Name) (ctor : ConstructorVal) (parents : Nat) : MetaM (Array NameInfo) := do
-  let type := ctor.type
-  let (fieldFunction, _) := dropArgs type (ctor.numParams + parents)
-  let (_, fields) := dropArgs fieldFunction (ctor.numFields - parents)
-  let mut fieldInfos := #[]
-  for (name, type) in fields do
-    fieldInfos := fieldInfos.push <| ← NameInfo.ofTypedName (struct.append name) type
-  return fieldInfos
-
-def StructureInfo.ofInductiveVal (v : InductiveVal) : MetaM StructureInfo := do
-  let info ← Info.ofConstantVal v.toConstantVal
-  let env ← getEnv
-  let parents := getParentStructures env v.name
-  let ctorVal := getStructureCtor env v.name
-  let ctor ← NameInfo.ofTypedName ctorVal.name ctorVal.type
-  match getStructureInfo? env v.name with
-  | some i =>
-    if i.fieldNames.size - parents.size > 0 then
-      return {
-        toInfo := info,
-        fieldInfo := ← getFieldTypes v.name ctorVal parents.size,
-        parents,
-        ctor
-      }
-    else
-      return {
-        toInfo := info,
-        fieldInfo := #[],
-        parents,
-        ctor
-      }
-  | none => panic! s!"{v.name} is not a structure"
-
-end DocGen4.Process

DocGen4/Process/TheoremInfo.lean

@@ -1,19 +0,0 @@
-/-
-Copyright (c) 2022 Henrik Böving. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-import Lean
-
-import DocGen4.Process.Base
-import DocGen4.Process.NameInfo
-
-namespace DocGen4.Process
-
-open Lean Meta
-
-def TheoremInfo.ofTheoremVal (v : TheoremVal) : MetaM TheoremInfo := do
-  let info ← Info.ofConstantVal v.toConstantVal
-  return { toInfo := info }
-
-end DocGen4.Process

Main.lean

@@ -11,16 +11,12 @@ def getTopLevelModules (p : Parsed) : IO (List String) :=  do
   return topLevelModules
 
 def runSingleCmd (p : Parsed) : IO UInt32 := do
-  let relevantModules := [p.positionalArg! "module" |>.as! String |> String.toName]
-  let res ← lakeSetup
-  match res with
-  | Except.ok ws =>
-    let (doc, hierarchy) ← load <| .loadAllLimitAnalysis relevantModules
-    IO.println "Outputting HTML"
-    let baseConfig ← getSimpleBaseContext hierarchy
-    htmlOutputResults baseConfig doc ws (p.hasFlag "ink")
-    return 0
-  | Except.error rc => pure rc
+  let relevantModules := #[p.positionalArg! "module" |>.as! String |> String.toName]
+  let gitUrl := p.positionalArg! "gitUrl" |>.as! String
+  let (doc, hierarchy) ← load <| .loadAllLimitAnalysis relevantModules
+  let baseConfig ← getSimpleBaseContext hierarchy
+  htmlOutputResults baseConfig doc (some gitUrl) (p.hasFlag "ink")
+  return 0
 
 def runIndexCmd (_p : Parsed) : IO UInt32 := do
   let hierarchy ← Hierarchy.fromDirectory Output.basePath
@@ -29,15 +25,10 @@ def runIndexCmd (_p : Parsed) : IO UInt32 := do
   return 0
 
 def runGenCoreCmd (_p : Parsed) : IO UInt32 := do
-  let res ← lakeSetup
-  match res with
-  | Except.ok ws =>
-    let (doc, hierarchy) ← loadCore
-    IO.println "Outputting HTML"
-    let baseConfig ← getSimpleBaseContext hierarchy
-    htmlOutputResults baseConfig doc ws (ink := False) 
-    return 0
-  | Except.error rc => pure rc
+  let (doc, hierarchy) ← loadCore
+  let baseConfig ← getSimpleBaseContext hierarchy
+  htmlOutputResults baseConfig doc none (ink := False)
+  return 0
 
 def runDocGenCmd (_p : Parsed) : IO UInt32 := do
   IO.println "You most likely want to use me via Lake now, check my README on Github on how to:"
@@ -53,6 +44,7 @@ def singleCmd := `[Cli|
 
   ARGS:
     module : String; "The module to generate the HTML for. Does not have to be part of topLevelModules."
+    gitUrl : String; "The gitUrl as computed by the Lake facet"
 ]
 
 def indexCmd := `[Cli|

Makefile

@@ -1,14 +0,0 @@
-all:
-	@echo "Please specify a build target."
-
-docs:
-	-ls build/doc | \
-		grep -v -E 'Init|Lean|Mathlib' | \
-		xargs -I {} rm -r "build/doc/{}"
-	-./scripts/run_pdflatex.sh build > /dev/null
-	lake build Bookshelf:docs
-
-docs!:
-	-rm -r build/doc
-	-./scripts/run_pdflatex.sh build > /dev/null
-	lake build Bookshelf:docs

README.md

@@ -1,7 +1,11 @@
 # bookshelf
 
-A study of the books listed below. Most proofs are conducted in LaTeX. Where
-feasible, theorems are also formally proven in [Lean](https://leanprover.github.io/).
+A study of the books listed below.
+
+## Overview
+
+Most proofs are conducted in LaTeX. Where feasible, theorems are also formally
+proven in [Lean](https://leanprover.github.io/).
 
 - [ ] Apostol, Tom M. Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. 2nd ed. Vol. 1. 2 vols. Wiley, 1991.
 - [x] Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
@@ -14,23 +18,21 @@ feasible, theorems are also formally proven in [Lean](https://leanprover.github.
 - [ ] Ross, Sheldon. A First Course in Probability Theory. 8th ed. Pearson Prentice Hall, n.d.
 - [ ] Smullyan, Raymond M. To Mock a Mockingbird: And Other Logic Puzzles Including an Amazing Adventure in Combinatory Logic. Oxford: Oxford university press, 2000.
 
-## Documentation
-
-This project has absorbed [doc-gen4](https://github.com/leanprover/doc-gen4) to
-ease customization. In particular, the `DocGen4` module found in this project
-allows generating PDFs and including them in the navbar. To generate
-documentation and serve files locally, run the following:
+## Building
 
+[direnv](https://direnv.net/) can be used to launch a dev shell upon entering
+this directory (refer to `.envrc`). Otherwise run via:
 ```bash
-> make docs[!]
-> lake run server
+$ nix develop
 ```
-
-The `docs` build target avoids cleaning files that are expected to not change
-often (e.g. `Lean`, `Init`, and `Mathlib` related content). If you've upgraded
-Lean or Mathlib, run `make docs!` instead to generate documentation from
-scratch.
-
-Both assume you have `pdflatex` and `python3` available in your `$PATH`. To
-change how the server behaves, refer to the `.env` file located in the root
-directory of this project.
+If you prefer not to use `nix`, you can also use the [elan](https://github.com/leanprover/elan)
+package manager like normal. Afterward, build the project by running
+```bash
+$ lake build
+```
+Optionally build documentation by running:
+```bash
+$ lake build Bookshelf:docs
+```
+Afterward, you can view the generated files by running `python3 -m http.server`
+from within the `.lake/build/doc` directory.

flake.lock

@@ -0,0 +1,76 @@
+{
+  "nodes": {
+    "flake-compat": {
+      "locked": {
+        "lastModified": 1696426674,
+        "narHash": "sha256-kvjfFW7WAETZlt09AgDn1MrtKzP7t90Vf7vypd3OL1U=",
+        "rev": "0f9255e01c2351cc7d116c072cb317785dd33b33",
+        "revCount": 57,
+        "type": "tarball",
+        "url": "https://api.flakehub.com/f/pinned/edolstra/flake-compat/1.0.1/018afb31-abd1-7bff-a5e4-cff7e18efb7a/source.tar.gz"
+      },
+      "original": {
+        "type": "tarball",
+        "url": "https://flakehub.com/f/edolstra/flake-compat/1.tar.gz"
+      }
+    },
+    "flake-utils": {
+      "inputs": {
+        "systems": "systems"
+      },
+      "locked": {
+        "lastModified": 1701680307,
+        "narHash": "sha256-kAuep2h5ajznlPMD9rnQyffWG8EM/C73lejGofXvdM8=",
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "rev": "4022d587cbbfd70fe950c1e2083a02621806a725",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1702312524,
+        "narHash": "sha256-gkZJRDBUCpTPBvQk25G0B7vfbpEYM5s5OZqghkjZsnE=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "a9bf124c46ef298113270b1f84a164865987a91c",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixos-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "flake-compat": "flake-compat",
+        "flake-utils": "flake-utils",
+        "nixpkgs": "nixpkgs"
+      }
+    },
+    "systems": {
+      "locked": {
+        "lastModified": 1681028828,
+        "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
+        "owner": "nix-systems",
+        "repo": "default",
+        "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nix-systems",
+        "repo": "default",
+        "type": "github"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

flake.nix

@@ -0,0 +1,79 @@
+{
+  description = "";
+
+  inputs = {
+    flake-compat.url = "https://flakehub.com/f/edolstra/flake-compat/1.tar.gz";
+    flake-utils.url = "github:numtide/flake-utils";
+    nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
+  };
+
+  outputs = { self, nixpkgs, flake-utils, ... }:
+    flake-utils.lib.eachDefaultSystem (system:
+      let
+        pkgs = nixpkgs.legacyPackages.${system};
+        manifest = import ./lake-manifest.nix { inherit pkgs; };
+        scheme-custom = with pkgs; (texlive.combine {
+          inherit (texlive) scheme-basic
+            bigfoot
+            comment
+            enumitem
+            environ
+            etoolbox
+            fontawesome5
+            jknapltx
+            mathabx
+            mathabx-type1
+            metafont
+            ncctools
+            pgf
+            rsfs
+            soul
+            stmaryrd
+            tcolorbox
+            xcolor;
+        });
+      in
+      {
+        packages = {
+          app = pkgs.stdenv.mkDerivation {
+            pname = "bookshelf";
+            version = "0.1.0";
+            src = ./.;
+            nativeBuildInputs = with pkgs; [
+              git
+              lean4
+              scheme-custom
+            ];
+            buildPhase = ''
+              mkdir -p .lake/packages
+              ${pkgs.lib.foldlAttrs (s: key: val: s + ''
+                cp -a ${val}/src .lake/packages/${key}
+                chmod 755 .lake/packages/${key}/{,.git}
+              '') "" manifest}
+
+              export GIT_ORIGIN_URL="https://github.com/jrpotter/bookshelf.git"
+              export GIT_REVISION="${self.rev or "dirty"}"
+              lake build Bookshelf:docs
+
+              find .lake/build/doc \
+                \( -name "*.html.trace" -o -name "*.html.hash" \) \
+                -exec rm {} +
+            '';
+            installPhase = ''
+              mkdir $out
+              cp -a .lake/build/doc/* $out
+            '';
+          };
+
+          default = self.packages.${system}.app;
+        };
+
+        devShells.default = pkgs.mkShell {
+          packages = with pkgs; [
+            lean4
+            python3
+            scheme-custom
+          ];
+        };
+      });
+}

lake-manifest.json

@@ -1,75 +1,95 @@
-{"version": 5,
- "packagesDir": "lake-packages",
+{"version": 7,
+ "packagesDir": ".lake/packages",
  "packages":
- [{"git":
-   {"url": "https://github.com/xubaiw/CMark.lean",
-    "subDir?": null,
-    "rev": "0077cbbaa92abf855fc1c0413e158ffd8195ec77",
-    "opts": {},
-    "name": "CMark",
-    "inputRev?": "main",
-    "inherited": false}},
-  {"git":
-   {"url": "https://github.com/EdAyers/ProofWidgets4",
-    "subDir?": null,
-    "rev": "a0c2cd0ac3245a0dade4f925bcfa97e06dd84229",
-    "opts": {},
-    "name": "proofwidgets",
-    "inputRev?": "v0.0.13",
-    "inherited": true}},
-  {"git":
-   {"url": "https://github.com/fgdorais/lean4-unicode-basic",
-    "subDir?": null,
-    "rev": "2491e781ae478b6e6f1d86a7157f1c58fc50f895",
-    "opts": {},
-    "name": "«lean4-unicode-basic»",
-    "inputRev?": "main",
-    "inherited": false}},
-  {"git":
-   {"url": "https://github.com/mhuisi/lean4-cli",
-    "subDir?": null,
-    "rev": "21dac2e9cc7e3cf7da5800814787b833e680b2fd",
-    "opts": {},
-    "name": "Cli",
-    "inputRev?": "nightly",
-    "inherited": false}},
-  {"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "43718b8bde561e133edfd4ab8b5def9fb438c18d",
-    "opts": {},
-    "name": "mathlib",
-    "inputRev?": "master",
-    "inherited": false}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "e75daed95ad1c92af4e577fea95e234d7a8401c1",
-    "opts": {},
-    "name": "Qq",
-    "inputRev?": "master",
-    "inherited": true}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "1a0cded2be292b5496e659b730d2accc742de098",
-    "opts": {},
-    "name": "aesop",
-    "inputRev?": "master",
-    "inherited": true}},
-  {"git":
-   {"url": "https://github.com/hargonix/LeanInk",
-    "subDir?": null,
-    "rev": "2447df5cc6e48eb965c3c3fba87e46d353b5e9f1",
-    "opts": {},
-    "name": "leanInk",
-    "inputRev?": "doc-gen",
-    "inherited": false}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4.git",
-    "subDir?": null,
-    "rev": "28459f72f3190b0f540b49ab769745819eeb1c5e",
-    "opts": {},
-    "name": "std",
-    "inputRev?": "main",
-    "inherited": false}}]}
+ [{"url": "https://github.com/leanprover/std4.git",
+   "type": "git",
+   "subDir": null,
+   "rev": "2e4a3586a8f16713f16b2d2b3af3d8e65f3af087",
+   "name": "std",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v4.3.0",
+   "inherited": false,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover-community/quote4",
+   "type": "git",
+   "subDir": null,
+   "rev": "d3a1d25f3eba0d93a58d5d3d027ffa78ece07755",
+   "name": "Qq",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "master",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover-community/aesop",
+   "type": "git",
+   "subDir": null,
+   "rev": "c7cff4551258d31c0d2d453b3f9cbca757d445f1",
+   "name": "aesop",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "master",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover-community/ProofWidgets4",
+   "type": "git",
+   "subDir": null,
+   "rev": "909febc72b4f64628f8d35cd0554f8a90b6e0749",
+   "name": "proofwidgets",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v0.0.23",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover/lean4-cli",
+   "type": "git",
+   "subDir": null,
+   "rev": "a751d21d4b68c999accb6fc5d960538af26ad5ec",
+   "name": "Cli",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "main",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover-community/mathlib4.git",
+   "type": "git",
+   "subDir": null,
+   "rev": "f04afed5ac9fea0e1355bc6f6bee2bd01f4a888d",
+   "name": "mathlib",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v4.3.0",
+   "inherited": false,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/xubaiw/CMark.lean",
+   "type": "git",
+   "subDir": null,
+   "rev": "0077cbbaa92abf855fc1c0413e158ffd8195ec77",
+   "name": "CMark",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "main",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/fgdorais/lean4-unicode-basic",
+   "type": "git",
+   "subDir": null,
+   "rev": "dc62b29a26fcc3da545472ab8ad2c98ef3433634",
+   "name": "UnicodeBasic",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "main",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/hargonix/LeanInk",
+   "type": "git",
+   "subDir": null,
+   "rev": "2447df5cc6e48eb965c3c3fba87e46d353b5e9f1",
+   "name": "leanInk",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "doc-gen",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/jrpotter/bookshelf-doc",
+   "type": "git",
+   "subDir": null,
+   "rev": "9bd217dc37ea79a3f118a313583f539cdbc762e6",
+   "name": "«doc-gen4»",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "main",
+   "inherited": false,
+   "configFile": "lakefile.lean"}],
+ "name": "bookshelf",
+ "lakeDir": ".lake"}

lake-manifest.nix

@@ -0,0 +1,119 @@
+{ pkgs }:
+let
+  fetchGitPackage = { pname, version, owner, repo, rev, hash }:
+    pkgs.stdenv.mkDerivation {
+      inherit pname version;
+      src = pkgs.fetchgit {
+        inherit rev hash;
+        url = "https://github.com/${owner}/${repo}";
+        # We need to keep this attribute enabled to prevent Lake from trying to
+        # update the package. This attribute ensures the specified commit is
+        # accessible at HEAD:
+        # https://github.com/leanprover/lean4/blob/cddc8089bc736a1532d6092f69476bd2d205a9eb/src/lake/Lake/Load/Materialize.lean#L22
+        leaveDotGit = true;
+      };
+      nativeBuildInputs = with pkgs; [ git ];
+      # Lake will perform a compulsory check that `git remote get-url origin`
+      # returns the value we set here:
+      # https://github.com/leanprover/lean4/blob/cddc8089bc736a1532d6092f69476bd2d205a9eb/src/lake/Lake/Load/Materialize.lean#L54
+      buildPhase = ''
+        git remote add origin https://github.com/${owner}/${repo}
+      '';
+      installPhase = ''
+        shopt -s dotglob
+        mkdir -p $out/src
+        cp -a . $out/src
+      '';
+    };
+in
+{
+  CMark = fetchGitPackage {
+    pname = "CMark";
+    version = "main";
+    owner = "xubaiw";
+    repo = "CMark.lean";
+    rev = "0077cbbaa92abf855fc1c0413e158ffd8195ec77";
+    hash = "sha256-ge+9V4IsMdPwjhYu66zUUN6CK70K2BdMT98BzBV3a4c=";
+  };
+
+  Cli = fetchGitPackage {
+    pname = "Cli";
+    version = "main";
+    owner = "leanprover";
+    repo = "lean4-cli";
+    rev = "a751d21d4b68c999accb6fc5d960538af26ad5ec";
+    hash = "sha256-n+6x7ZhyKKiIMZ9cH9VV8zay3oTUlJojtxcLYsUwQPU=";
+  };
+
+  Qq = fetchGitPackage {
+    pname = "Qq";
+    version = "master";
+    owner = "leanprover-community";
+    repo = "quote4";
+    rev = "d3a1d25f3eba0d93a58d5d3d027ffa78ece07755";
+    hash = "sha256-l+X+Mi4khC/xdwQmESz8Qzto6noYqhYN4UqC+TVt3cs=";
+  };
+
+  UnicodeBasic = fetchGitPackage {
+    pname = "UnicodeBasic";
+    version = "main";
+    owner = "fgdorais";
+    repo = "lean4-unicode-basic";
+    rev = "dc62b29a26fcc3da545472ab8ad2c98ef3433634";
+    hash = "sha256-EimohrYMr01CnGx8xCg4q4XX663QuxKfpTDNnDnosO4=";
+  };
+
+  aesop = fetchGitPackage {
+    pname = "aesop";
+    version = "master";
+    owner = "leanprover-community";
+    repo = "aesop";
+    rev = "c7cff4551258d31c0d2d453b3f9cbca757d445f1";
+    hash = "sha256-uzkxE9XJ4y3WMtmiNQn2Je1hNkQ2FgE1/0vqz8f98cw=";
+  };
+
+  doc-gen4 = fetchGitPackage {
+    pname = "doc-gen4";
+    version = "main";
+    owner = "jrpotter";
+    repo = "bookshelf-doc";
+    rev = "9bd217dc37ea79a3f118a313583f539cdbc762e6";
+    hash = "sha256-L7Uca5hJV19/WHYG+MkFWX6BwXDInfSYsOrnZdM9ejY=";
+  };
+
+  leanInk = fetchGitPackage {
+    pname = "leanInk";
+    version = "doc-gen";
+    owner = "hargonix";
+    repo = "LeanInk";
+    rev = "2447df5cc6e48eb965c3c3fba87e46d353b5e9f1";
+    hash = "sha256-asHVaa1uOxpz5arCvfllIrJmMC9VDm1F+bufsu3XwN0=";
+  };
+
+  mathlib = fetchGitPackage {
+    pname = "mathlib";
+    version = "v4.3.0";
+    owner = "leanprover-community";
+    repo = "mathlib4.git";
+    rev = "f04afed5ac9fea0e1355bc6f6bee2bd01f4a888d";
+    hash = "sha256-B0pZ7HwJwOrEXTMMyJSzMLLyh66Bcs/CqNwC3EKZ60I=";
+  };
+
+  proofwidgets = fetchGitPackage {
+    pname = "proofwidgets";
+    version = "v0.0.23";
+    owner = "leanprover-community";
+    repo = "ProofWidgets4";
+    rev = "909febc72b4f64628f8d35cd0554f8a90b6e0749";
+    hash = "sha256-twXXKXXONQpfzG+YLoXYY+3kTU0F40Tsv2+SKfF2Qsc=";
+  };
+
+  std = fetchGitPackage {
+    pname = "std";
+    version = "v4.3.0";
+    owner = "leanprover";
+    repo = "std4";
+    rev = "2e4a3586a8f16713f16b2d2b3af3d8e65f3af087";
+    hash = "sha256-agWcsRIEJbHSjIdiA6z/HQHLZkb72ASW9SPnIM0voeo=";
+  };
+}

lakefile.lean

@@ -4,165 +4,17 @@ open System Lake DSL
 
 package «bookshelf»
 
--- ========================================
--- Imports
--- ========================================
-
-require Cli from git
-  "https://github.com/mhuisi/lean4-cli" @
-    "nightly"
-require CMark from git
-  "https://github.com/xubaiw/CMark.lean" @
-    "main"
-require «lean4-unicode-basic» from git
-  "https://github.com/fgdorais/lean4-unicode-basic" @
-    "main"
-require leanInk from git
-  "https://github.com/hargonix/LeanInk" @
-    "doc-gen"
 require mathlib from git
   "https://github.com/leanprover-community/mathlib4.git" @
-    "master"
+    "v4.3.0"
 require std from git
   "https://github.com/leanprover/std4.git" @
+    "v4.3.0"
+require «doc-gen4» from git
+  "https://github.com/jrpotter/bookshelf-doc" @
     "main"
 
--- ========================================
--- Documentation Generator
--- ========================================
-
-lean_lib DocGen4
-
-lean_exe «doc-gen4» {
-  root := `Main
-  supportInterpreter := true
-}
-
-module_facet docs (mod) : FilePath := do
-  let some docGen4 ← findLeanExe? `«doc-gen4»
-    | error "no doc-gen4 executable configuration found in workspace"
-  let exeJob ← docGen4.exe.fetch
-  let modJob ← mod.leanBin.fetch
-  let buildDir := (← getWorkspace).root.buildDir
-  let docFile := mod.filePath (buildDir / "doc") "html"
-  exeJob.bindAsync fun exeFile exeTrace => do
-  modJob.bindSync fun _ modTrace => do
-    let depTrace := exeTrace.mix modTrace
-    let trace ← buildFileUnlessUpToDate docFile depTrace do
-      logInfo s!"Documenting module: {mod.name}"
-      proc {
-        cmd := exeFile.toString
-        args := #["single", mod.name.toString]
-        env := #[("LEAN_PATH", (← getAugmentedLeanPath).toString)]
-      }
-    return (docFile, trace)
-
--- TODO: technically speaking this facet does not show all file dependencies
-target coreDocs : FilePath := do
-  let some docGen4 ← findLeanExe? `«doc-gen4»
-    | error "no doc-gen4 executable configuration found in workspace"
-  let exeJob ← docGen4.exe.fetch
-  let basePath := (←getWorkspace).root.buildDir / "doc"
-  let dataFile := basePath / "declarations" / "declaration-data-Lean.bmp"
-  exeJob.bindSync fun exeFile exeTrace => do
-    let trace ← buildFileUnlessUpToDate dataFile exeTrace do
-      logInfo "Documenting Lean core: Init and Lean"
-      proc {
-        cmd := exeFile.toString
-        args := #["genCore"]
-        env := #[("LEAN_PATH", (← getAugmentedLeanPath).toString)]
-      }
-    return (dataFile, trace)
-
-library_facet docs (lib) : FilePath := do
-  -- Ordering is important. The index file is generated by walking through the
-  -- filesystem directory. Files copied from the shell scripts need to exist
-  -- prior to this.
-  let mods ← lib.modules.fetch
-  let moduleJobs ← BuildJob.mixArray <| ← mods.mapM (fetch <| ·.facet `docs)
-  let coreJob : BuildJob FilePath ← coreDocs.fetch
-  let exeJob ← «doc-gen4».fetch
-  -- Shared with DocGen4.Output
-  let basePath := (←getWorkspace).root.buildDir / "doc"
-  let dataFile := basePath / "declarations" / "declaration-data.bmp"
-  let staticFiles := #[
-    basePath / "style.css",
-    basePath / "declaration-data.js",
-    basePath / "color-scheme.js",
-    basePath / "nav.js",
-    basePath / "how-about.js",
-    basePath / "search.js",
-    basePath / "mathjax-config.js",
-    basePath / "instances.js",
-    basePath / "importedBy.js",
-    basePath / "index.html",
-    basePath / "404.html",
-    basePath / "navbar.html",
-    basePath / "search.html",
-    basePath / "find" / "index.html",
-    basePath / "find" / "find.js",
-    basePath / "src"  / "alectryon.css",
-    basePath / "src"  / "alectryon.js",
-    basePath / "src"  / "docutils_basic.css",
-    basePath / "src"  / "pygments.css"
-  ]
-  coreJob.bindAsync fun _ coreInputTrace => do
-    exeJob.bindAsync fun exeFile exeTrace => do
-      moduleJobs.bindSync fun _ inputTrace => do
-        let depTrace := mixTraceArray #[inputTrace, exeTrace, coreInputTrace]
-        let trace ← buildFileUnlessUpToDate dataFile depTrace do
-          logInfo "Documentation indexing"
-          proc {
-            cmd := exeFile.toString
-            args := #["index"]
-          }
-        let traces ← staticFiles.mapM computeTrace
-        let indexTrace := mixTraceArray traces
-
-        return (dataFile, trace.mix indexTrace)
-
--- ========================================
--- Bookshelf
--- ========================================
-
 @[default_target]
 lean_lib «Bookshelf» {
   roots := #[`Bookshelf, `Common]
 }
-
-/--
-The contents of our `.env` file.
--/
-structure Config where
-  port : Nat := 5555
-
-/--
-Read in the `.env` file into an in-memory structure.
--/
-private def readConfig : StateT Config ScriptM Unit := do
-  let env <- IO.FS.readFile ".env"
-  for line in env.trim.split (fun c => c == '\n') do
-    match line.split (fun c => c == '=') with
-    | ["PORT", port] => modify (fun c => { c with port := String.toNat! port })
-    | _ => error "Malformed `.env` file."
-  return ()
-
-/--
-Start an HTTP server for locally serving documentation. It is expected the
-documentation has already been generated prior via
-
-```bash
-> lake build Bookshelf:docs
-```
-
-USAGE:
-  lake run server
--/
-script server (_args) do
-  let ((), config) <- StateT.run readConfig {}
-  IO.println s!"Running Lean on `http://localhost:{config.port}`"
-  _ <- IO.Process.run {
-    cmd := "python3",
-    args := #["-m", "http.server", toString config.port, "-d", "build/doc"],
-  }
-  return 0

lean-toolchain

@@ -1 +1 @@
-leanprover/lean4:4.0.0
+leanprover/lean4:v4.3.0

preamble.tex

@@ -170,7 +170,7 @@
 \newcommand{\ceil}[1]{\left\lceil#1\right\rceil}
 \newcommand{\ctuple}[2]{\left< #1, \cdots, #2 \right>}
 \newcommand{\dom}[1]{\textop{dom}{#1}}
-\newcommand{\equinumerous}[2]{#1 \approx #2}
+\newcommand{\equin}{\approx}
 \newcommand{\fld}[1]{\textop{fld}{#1}}
 \newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
 \newcommand{\icc}[2]{\left[#1, #2\right]}

scripts/run_pdflatex.sh

@@ -1,26 +0,0 @@
-#!/usr/bin/env bash
-
-if ! command -v pdflatex > /dev/null; then
-  >&2 echo 'pdflatex was not found in the current $PATH.'
-  exit 1
-fi
-
-BUILD_DIR="$1"
-
-function process_file () {
-  REL_DIR=$(dirname "$1")
-  REL_BASE=$(basename -s ".tex" "$1")
-  mkdir -p "$BUILD_DIR/doc/$REL_DIR"
-  (cd "$REL_DIR" && pdflatex "$REL_BASE.tex")
-  cp "$REL_DIR/$REL_BASE.pdf" "$BUILD_DIR/doc/$REL_DIR/"
-}
-
-export BUILD_DIR
-export -f process_file
-
-# We run this command twice to allow any cross-references to resolve correctly.
-# https://tex.stackexchange.com/questions/41539/does-hyperref-work-between-two-files
-for _ in {1..2}; do
-  find ./* \( -path build -o -path lake-packages \) -prune -o -name "*.tex" -print0 \
-    | xargs -0 -I{} bash -c "process_file {}"
-done

static/alectryon/alectryon.css

@@ -1,777 +0,0 @@
-@charset "UTF-8";
-/*
-Copyright © 2019 Clément Pit-Claudel
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in all
-copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-SOFTWARE.
-*/
-
-/*******************************/
-/* CSS reset for .alectryon-io */
-/*******************************/
-
-.alectryon-io blockquote {
-    line-height: inherit;
-}
-
-.alectryon-io blockquote:after {
-    display: none;
-}
-
-.alectryon-io label {
-    display: inline;
-    font-size: inherit;
-    margin: 0;
-}
-
-.alectryon-io a {
-    text-decoration: none !important;
-    font-style: oblique !important;
-    color: unset;
-}
-
-/* Undo <small> and <blockquote>, added to improve RSS rendering. */
-
-.alectryon-io small.alectryon-output,
-.alectryon-io small.alectryon-type-info {
-    font-size: inherit;
-}
-
-.alectryon-io blockquote.alectryon-goal,
-.alectryon-io blockquote.alectryon-message {
-    font-weight: normal;
-    font-size: inherit;
-}
-
-/***************/
-/* Main styles */
-/***************/
-
-.alectryon-coqdoc .doc .code,
-.alectryon-coqdoc .doc .comment,
-.alectryon-coqdoc .doc .inlinecode,
-.alectryon-mref,
-.alectryon-block, .alectryon-io,
-.alectryon-toggle-label, .alectryon-banner {
-    font-family: "Source Code Pro", Consolas, "Ubuntu Mono", Menlo, "DejaVu Sans Mono", monospace, monospace !important;
-    font-size: 0.875em;
-    font-feature-settings: "COQX" 1 /* Coq ligatures */, "XV00" 1 /* Legacy */, "calt" 1 /* Fallback */;
-    line-height: initial;
-}
-
-.alectryon-io, .alectryon-block, .alectryon-toggle-label, .alectryon-banner {
-    overflow: visible;
-    overflow-wrap: break-word;
-    position: relative;
-    white-space: pre-wrap;
-}
-
-/*
-CoqIDE doesn't turn off the unicode bidirectional algorithm (and PG simply
-respects the user's `bidi-display-reordering` setting), so don't turn it off
-here either.  But beware unexpected results like `Definition test_אב := 0.`
-
-.alectryon-io span {
-    direction: ltr;
-    unicode-bidi: bidi-override;
-}
-
-In any case, make an exception for comments:
-
-.highlight .c {
-    direction: embed;
-    unicode-bidi: initial;
-}
-*/
-
-.alectryon-mref,
-.alectryon-mref-marker {
-    align-self: center;
-    box-sizing: border-box;
-    display: inline-block;
-    font-size: 80%;
-    font-weight: bold;
-    line-height: 1;
-    box-shadow: 0 0 0 1pt black;
-    padding: 1pt 0.3em;
-    text-decoration: none;
-}
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-.alectryon-block .alectryon-mref-marker,
-.alectryon-io .alectryon-mref-marker {
-    user-select: none;
-    margin: -0.25em 0 -0.25em 0.5em;
-}
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-.alectryon-inline .alectryon-mref-marker {
-    margin: -0.25em 0.15em -0.25em 0.625em; /* 625 = 0.5em / 80% */
-}
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-.alectryon-mref {
-    color: inherit;
-    margin: -0.5em 0.25em;
-}
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-.alectryon-goal:target .goal-separator .alectryon-mref-marker,
-:target > .alectryon-mref-marker {
-    animation: blink 0.2s step-start 0s 3 normal none;
-    background-color: #fcaf3e;
-    position: relative;
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-
-@keyframes blink {
-    50% {
-        box-shadow: 0 0 0 3pt #fcaf3e, 0 0 0 4pt black;
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-.alectryon-toggle,
-.alectryon-io .alectryon-extra-goal-toggle {
-    display: none;
-}
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-.alectryon-bubble,
-.alectryon-io label,
-.alectryon-toggle-label {
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-.alectryon-toggle-label {
-    display: block;
-    font-size: 0.8em;
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-.alectryon-io .alectryon-input {
-    padding: 0.1em 0; /* Enlarge the hitbox slightly to fill interline gaps */
-}
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-.alectryon-io .alectryon-token {
-    white-space: pre-wrap;
-    display: inline;
-}
-
-.alectryon-io .alectryon-sentence.alectryon-target .alectryon-input {
-    /* FIXME if keywords were ‘bolder’ we wouldn't need !important */
-    font-weight: bold !important; /* Use !important to avoid a * selector */
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-.alectryon-bubble:before,
-.alectryon-toggle-label:before,
-.alectryon-io label.alectryon-input:after,
-.alectryon-io .alectryon-goal > label:before {
-    border: 1px solid #babdb6;
-    border-radius: 1em;
-    box-sizing: border-box;
-    content: '';
-    display: inline-block;
-    font-weight: bold;
-    height: 0.25em;
-    margin-bottom: 0.15em;
-    vertical-align: middle;
-    width: 0.75em;
-}
-
-.alectryon-toggle-label:before,
-.alectryon-io .alectryon-goal > label:before {
-    margin-right: 0.25em;
-}
-
-.alectryon-io .alectryon-goal > label:before {
-    margin-top: 0.125em;
-}
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-.alectryon-io label.alectryon-input {
-    padding-right: 1em; /* Prevent line wraps before the checkbox bubble */
-}
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-.alectryon-io label.alectryon-input:after {
-    margin-left: 0.25em;
-    margin-right: -1em; /* Compensate for the anti-wrapping space */
-}
-
-.alectryon-failed {
-    /* Underlines are broken in Chrome (they reset at each element boundary)… */
-    /* text-decoration: red wavy underline; */
-    /* … but it isn't too noticeable with dots */
-    text-decoration: red dotted underline;
-    text-decoration-skip-ink: none;
-    /* Chrome prints background images in low resolution, yielding a blurry underline */
-    /* background: bottom / 0.3em auto repeat-x url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAyLjY0NiAxLjg1MiIgaGVpZ2h0PSI4IiB3aWR0aD0iMTAiPjxwYXRoIGQ9Ik0wIC4yNjVjLjc5NCAwIC41MyAxLjMyMiAxLjMyMyAxLjMyMi43OTQgMCAuNTMtMS4zMjIgMS4zMjMtMS4zMjIiIGZpbGw9Im5vbmUiIHN0cm9rZT0icmVkIiBzdHJva2Utd2lkdGg9Ii41MjkiLz48L3N2Zz4=); */
-}
-
-/* Wrapping :hover rules in a media query ensures that tapping a Coq sentence
-   doesn't trigger its :hover state (otherwise, on mobile, tapping a sentence to
-   hide its output causes it to remain visible (its :hover state gets triggered.
-   We only do it for the default style though, since other styles don't put the
-   output over the main text, so showing too much is not an issue. */
-@media (any-hover: hover) {
-    .alectryon-bubble:hover:before,
-    .alectryon-toggle-label:hover:before,
-    .alectryon-io label.alectryon-input:hover:after {
-        background: #eeeeec;
-    }
-
-    .alectryon-io label.alectryon-input:hover {
-        text-decoration: underline dotted #babdb6;
-	    text-shadow: 0 0 1px rgb(46, 52, 54, 0.3); /* #2e3436 + opacity */
-    }
-
-    .alectryon-io .alectryon-sentence:hover .alectryon-output,
-    .alectryon-io .alectryon-token:hover .alectryon-type-info-wrapper,
-    .alectryon-io .alectryon-token:hover .alectryon-type-info-wrapper {
-        z-index: 2; /* Place hovered goals above .alectryon-sentence.alectryon-target ones */
-    }
-}
-
-.alectryon-toggle:checked + .alectryon-toggle-label:before,
-.alectryon-io .alectryon-sentence > .alectryon-toggle:checked + label.alectryon-input:after,
-.alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal > label:before {
-    background-color: #babdb6;
-    border-color: #babdb6;
-}
-
-/* Disable clicks on sentences when the document-wide toggle is set. */
-.alectryon-toggle:checked + label + .alectryon-container label.alectryon-input {
-    cursor: unset;
-    pointer-events: none;
-}
-
-/* Hide individual checkboxes when the document-wide toggle is set. */
-.alectryon-toggle:checked + label + .alectryon-container label.alectryon-input:after {
-    display: none;
-}
-
-/* .alectryon-output is displayed by toggles, :hover, and .alectryon-target rules */
-.alectryon-io .alectryon-output {
-    box-sizing: border-box;
-    display: none;
-    left: 0;
-    right: 0;
-    position: absolute;
-    padding: 0.25em 0;
-    overflow: visible; /* Let box-shadows overflow */
-    z-index: 1; /* Default to an index lower than that used by :hover */
-}
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-.alectryon-io .alectryon-type-info-wrapper {
-    position: absolute;
-    display: inline-block;
-    width: 100%;
-}
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-.alectryon-io .alectryon-type-info-wrapper.full-width {
-    left: 0;
-    min-width: 100%;
-    max-width: 100%;
-}
-
-.alectryon-io .alectryon-type-info .goal-separator {
-    height: unset;
-    margin-top: 0em;
-}
-
-.alectryon-io .alectryon-type-info-wrapper .alectryon-type-info {
-    box-sizing: border-box;
-    bottom: 100%;
-    position: absolute;
-    /*padding: 0.25em 0;*/
-    visibility: hidden;
-    overflow: visible; /* Let box-shadows overflow */
-    z-index: 1; /* Default to an index lower than that used by :hover */
-    white-space: pre-wrap !important;
-}
-
-.alectryon-io .alectryon-type-info-wrapper .alectryon-type-info .alectryon-goal.alectryon-docstring {
-    white-space: pre-wrap !important;
-}
-
-@media (any-hover: hover) { /* See note above about this @media query */
-    .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) {
-        display: block;
-    }
-
-    .alectryon-io.output-hidden .alectryon-sentence:hover .alectryon-output:not(:hover) {
-        display: none !important;
-    }
-
-    .alectryon-io.type-info-hidden .alectryon-token:hover .alectryon-type-info-wrapper .alectryon-type-info,
-    .alectryon-io.type-info-hidden .alectryon-token:hover .alectryon-type-info-wrapper .alectryon-type-info {
-        /*visibility: hidden !important;*/
-    }
-
-    .alectryon-io .alectryon-token:hover .alectryon-type-info-wrapper .alectryon-type-info,
-    .alectryon-io .alectryon-token:hover .alectryon-type-info-wrapper .alectryon-type-info {
-        visibility: visible;
-        transition-delay: 0.5s;
-    }
-}
-
-.alectryon-io .alectryon-sentence.alectryon-target .alectryon-output {
-    display: block;
-}
-
-/* Indicate active (hovered or targeted) goals with a shadow. */
-.alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-messages,
-.alectryon-io .alectryon-sentence.alectryon-target .alectryon-output  .alectryon-messages,
-.alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-goals,
-.alectryon-io .alectryon-sentence.alectryon-target .alectryon-output  .alectryon-goals,
-.alectryon-io .alectryon-token:hover .alectryon-type-info-wrapper .alectryon-type-info {
-    box-shadow: 2px 2px 2px gray;
-}
-
-.alectryon-io .alectryon-extra-goals .alectryon-goal .goal-hyps {
-    display: none;
-}
-
-.alectryon-io .alectryon-extra-goals .alectryon-extra-goal-toggle:not(:checked) + .alectryon-goal label.goal-separator hr {
-    /* Dashes indicate that the hypotheses are hidden */
-    border-top-style: dashed;
-}
-
-
-/* Show just a small preview of the other goals; this is undone by the
-   "extra-goal" toggle and by :hover and .alectryon-target in windowed mode. */
-.alectryon-io .alectryon-extra-goals .alectryon-goal .goal-conclusion {
-    max-height: 5.2em;
-    overflow-y: auto;
-    /* Combining ‘overflow-y: auto’ with ‘display: inline-block’ causes extra space
-       to be added below the box. ‘vertical-align: middle’ gets rid of it. */
-    vertical-align: middle;
-}
-
-.alectryon-io .alectryon-goals,
-.alectryon-io .alectryon-messages {
-    background: #f6f7f6;
-	/*border: thin solid #d3d7cf; /* Convenient when pre's background is already #EEE */
-    display: block;
-    padding: 0.25em;
-}
-
-.alectryon-message::before {
-    content: '';
-    float: right;
-    /* etc/svg/square-bubble-xl.svg */
-    background: url("data:image/svg+xml,%3Csvg width='14' height='14' viewBox='0 0 3.704 3.704' xmlns='http://www.w3.org/2000/svg'%3E%3Cg fill-rule='evenodd' stroke='%23000' stroke-width='.264'%3E%3Cpath d='M.794.934h2.115M.794 1.463h1.455M.794 1.992h1.852'/%3E%3C/g%3E%3Cpath d='M.132.14v2.646h.794v.661l.926-.661h1.72V.14z' fill='none' stroke='%23000' stroke-width='.265'/%3E%3C/svg%3E") top right no-repeat;
-    height: 14px;
-    width: 14px;
-}
-
-.alectryon-toggle:checked + label + .alectryon-container {
-    width: unset;
-}
-
-/* Show goals when a toggle is set */
-.alectryon-toggle:checked + label + .alectryon-container label.alectryon-input + .alectryon-output,
-.alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output {
-    display: block;
-    position: static;
-    width: unset;
-    background: unset; /* Override the backgrounds set in floating in windowed mode */
-    padding: 0.25em 0; /* Re-assert so that later :hover rules don't override this padding */
-}
-
-.alectryon-toggle:checked + label + .alectryon-container label.alectryon-input + .alectryon-output .goal-hyps,
-.alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output .goal-hyps {
-    /* Overridden back in windowed style */
-    flex-flow: row wrap;
-    justify-content: flex-start;
-}
-
-.alectryon-toggle:checked + label + .alectryon-container .alectryon-sentence .alectryon-output > div,
-.alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output > div {
-    display: block;
-}
-
-.alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal .goal-hyps {
-    display: flex;
-}
-
-.alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal .goal-conclusion {
-    max-height: unset;
-    overflow-y: unset;
-}
-
-.alectryon-toggle:checked + label + .alectryon-container .alectryon-sentence > .alectryon-toggle ~ .alectryon-wsp,
-.alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-wsp {
-    display: none;
-}
-
-.alectryon-io .alectryon-messages,
-.alectryon-io .alectryon-message,
-.alectryon-io .alectryon-goals,
-.alectryon-io .alectryon-goal,
-.alectryon-io .goal-hyps > span,
-.alectryon-io .goal-conclusion {
-    border-radius: 0.15em;
-}
-
-.alectryon-io .alectryon-goal,
-.alectryon-io .alectryon-message {
-    align-items: center;
-    background: #f6f7f6;
-    border: 0em;
-    display: block;
-    flex-direction: column;
-    margin: 0.25em;
-    padding: 0.5em;
-    position: relative;
-}
-
-.alectryon-io .goal-hyps {
-    align-content: space-around;
-    align-items: baseline;
-    display: flex;
-    flex-flow: column nowrap; /* re-stated in windowed mode */
-    justify-content: space-around;
-    /* LATER use a ‘gap’ property instead of margins once supported */
-    margin: -0.15em -0.25em; /* -0.15em to cancel the item spacing */
-    padding-bottom: 0.35em; /* 0.5em-0.15em to cancel the 0.5em of .goal-separator */
-}
-
-.alectryon-io .goal-hyps > br {
-    display: none; /* Only for RSS readers */
-}
-
-.alectryon-io .goal-hyps > span,
-.alectryon-io .goal-conclusion {
-    /*background: #eeeeec;*/
-    display: inline-block;
-    padding: 0.15em 0.35em;
-}
-
-.alectryon-io .goal-hyps > span {
-    align-items: baseline;
-    display: inline-flex;
-    margin: 0.15em 0.25em;
-}
-
-.alectryon-block var,
-.alectryon-inline var,
-.alectryon-io .goal-hyps > span > var {
-    font-weight: 600;
-    font-style: unset;
-}
-
-.alectryon-io .goal-hyps > span > var {
-    /* Shrink the list of names, but let it grow as long as space is available. */
-    flex-basis: min-content;
-    flex-grow: 1;
-}
-
-.alectryon-io .goal-hyps > span b {
-    font-weight: 600;
-    margin: 0 0 0 0.5em;
-    white-space: pre;
-}
-
-.alectryon-io .hyp-body,
-.alectryon-io .hyp-type {
-    display: flex;
-    align-items: baseline;
-}
-
-.alectryon-io .goal-separator {
-    align-items: center;
-    display: flex;
-    flex-direction: row;
-    height: 1em; /* Fixed height to ignore goal name and markers */
-    margin-top: -0.5em; /* Compensated in .goal-hyps when shown */
-}
-
-.alectryon-io .goal-separator hr {
-    border: none;
-    border-top: thin solid #555753;
-    display: block;
-    flex-grow: 1;
-    margin: 0;
-}
-
-.alectryon-io .goal-separator .goal-name {
-    font-size: 0.75em;
-    margin-left: 0.5em;
-}
-
-/**********/
-/* Banner */
-/**********/
-
-.alectryon-banner {
-    background: #eeeeec;
-    border: 1px solid #babcbd;
-    font-size: 0.75em;
-    padding: 0.25em;
-    text-align: center;
-    margin: 1em 0;
-}
-
-.alectryon-banner a {
-    cursor: pointer;
-    text-decoration: underline;
-}
-
-.alectryon-banner kbd {
-    background: #d3d7cf;
-    border-radius: 0.15em;
-    border: 1px solid #babdb6;
-    box-sizing: border-box;
-    display: inline-block;
-    font-family: inherit;
-    font-size: 0.9em;
-    height: 1.3em;
-    line-height: 1.2em;
-    margin: -0.25em 0;
-    padding: 0 0.25em;
-    vertical-align: middle;
-}
-
-/**********/
-/* Toggle */
-/**********/
-
-.alectryon-toggle-label {
-    margin: 1rem 0;
-}
-
-/******************/
-/* Floating style */
-/******************/
-
-/* If there's space, display goals to the right of the code, not below it. */
-@media (min-width: 80rem) {
-    /* Unlike the windowed case, we don't want to move output blocks to the side
-       when they are both :checked and -targeted, since it gets confusing as
-       things jump around; hence the commented-output part of the selector,
-       which would otherwise increase specificity */
-    .alectryon-floating .alectryon-sentence.alectryon-target /* > .alectryon-toggle ~ */ .alectryon-output,
-    .alectryon-floating .alectryon-sentence:hover .alectryon-output {
-        top: 0;
-        left: 100%;
-        right: -100%;
-        padding: 0 0.5em;
-        position:  absolute;
-    }
-
-    .alectryon-floating .alectryon-output {
-        min-height: 100%;
-    }
-
-    .alectryon-floating .alectryon-sentence:hover .alectryon-output {
-        background: white; /* Ensure that short goals hide long ones */
-    }
-
-    /* This odd margin-bottom property prevents the sticky div from bumping
-       against the bottom of its container (.alectryon-output).  The alternative
-       would be enlarging .alectryon-output, but that would cause overflows,
-       enlarging scrollbars and yielding scrolling towards the bottom of the
-       page.  Doing things this way instead makes it possible to restrict
-       .alectryon-output to a reasonable size (100%, through top = bottom = 0).
-       See also https://stackoverflow.com/questions/43909940/. */
-    /* See note on specificity above */
-    .alectryon-floating .alectryon-sentence.alectryon-target /* > .alectryon-toggle ~ */ .alectryon-output > div,
-    .alectryon-floating .alectryon-sentence:hover .alectryon-output > div {
-        margin-bottom: -200%;
-        position: sticky;
-        top: 0;
-    }
-
-    .alectryon-floating .alectryon-toggle:checked + label + .alectryon-container .alectryon-sentence .alectryon-output > div,
-    .alectryon-floating .alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output > div {
-        margin-bottom: unset; /* Undo the margin */
-    }
-
-    /* Float underneath the current fragment
-    @media (max-width: 80rem) {
-        .alectryon-floating .alectryon-output {
-            top: 100%;
-        }
-    } */
-}
-
-/********************/
-/* Multi-pane style */
-/********************/
-
-.alectryon-windowed {
-    border: 0 solid #2e3436;
-    box-sizing: border-box;
-}
-
-.alectryon-windowed .alectryon-sentence:hover .alectryon-output {
-    background: white; /* Ensure that short goals hide long ones */
-}
-
-.alectryon-windowed .alectryon-output {
-    position: fixed; /* Overwritten by the ‘:checked’ rules */
-}
-
-/* See note about specificity below */
-.alectryon-windowed .alectryon-sentence:hover .alectryon-output,
-.alectryon-windowed .alectryon-sentence.alectryon-target > .alectryon-toggle ~ .alectryon-output {
-    padding: 0.5em;
-    overflow-y: auto; /* Windowed contents may need to scroll */
-}
-
-.alectryon-windowed .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-messages,
-.alectryon-windowed .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output  .alectryon-messages,
-.alectryon-windowed .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-goals,
-.alectryon-windowed .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output  .alectryon-goals {
-    box-shadow: none; /* A shadow is unnecessary here and incompatible with overflow-y set to auto */
-}
-
-.alectryon-windowed .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output .goal-hyps {
-    /* Restated to override the :checked style */
-    flex-flow: column nowrap;
-    justify-content: space-around;
-}
-
-
-.alectryon-windowed .alectryon-sentence.alectryon-target .alectryon-extra-goals .alectryon-goal .goal-conclusion
-/* Like .alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal .goal-conclusion */ {
-    max-height: unset;
-    overflow-y: unset;
-}
-
-.alectryon-windowed .alectryon-output > div {
-    display: flex; /* Put messages after goals */
-    flex-direction: column-reverse;
-}
-
-/*********************/
-/* Standalone styles */
-/*********************/
-
-.alectryon-standalone {
-    font-family: 'IBM Plex Serif', 'PT Serif', 'Merriweather', 'DejaVu Serif', serif;
-    line-height: 1.5;
-}
-
-@media screen and (min-width: 50rem) {
-    html.alectryon-standalone {
-        /* Prevent flickering when hovering a block causes scrollbars to appear. */
-        margin-left: calc(100vw - 100%);
-        margin-right: 0;
-    }
-}
-
-/* Coqdoc */
-
-.alectryon-coqdoc .doc .code,
-.alectryon-coqdoc .doc .inlinecode,
-.alectryon-coqdoc .doc .comment {
-    display: inline;
-}
-
-.alectryon-coqdoc .doc .comment {
-    color: #eeeeec;
-}
-
-.alectryon-coqdoc .doc .paragraph {
-    height: 0.75em;
-}
-
-/* Centered, Floating */
-
-.alectryon-standalone .alectryon-centered,
-.alectryon-standalone .alectryon-floating {
-    max-width: 50rem;
-    margin: auto;
-}
-
-@media (min-width: 80rem) {
-    .alectryon-standalone .alectryon-floating {
-        max-width: 80rem;
-    }
-
-    .alectryon-standalone .alectryon-floating > * {
-        width: 50%;
-        margin-left: 0;
-    }
-}
-
-/* Windowed */
-
-.alectryon-standalone .alectryon-windowed {
-    display: block;
-    margin: 0;
-    overflow-y: auto;
-    position: absolute;
-    padding: 0 1em;
-}
-
-.alectryon-standalone .alectryon-windowed > * {
-    /* Override properties of docutils_basic.css */
-    margin-left: 0;
-    max-width: unset;
-}
-
-.alectryon-standalone .alectryon-windowed .alectryon-io {
-    box-sizing: border-box;
-    width: 100%;
-}
-
-/* No need to predicate the ‘:hover’ rules below on ‘:not(:checked)’, since ‘left’,
-   ‘right’, ‘top’, and ‘bottom’ will be inactived by the :checked rules setting
-   ‘position’ to ‘static’ */
-
-
-/* Specificity: We want the output to stay inline when hovered while unfolded
-   (:checked), but we want it to move when it's targeted (i.e. when the user
-   is browsing goals one by one using the keyboard, in which case we want to
-   goals to appear in consistent locations).  The selectors below ensure
-   that :hover < :checked < -targeted in terms of specificity. */
-/* LATER: Reimplement this stuff with CSS variables */
-.alectryon-windowed .alectryon-sentence.alectryon-target > .alectryon-toggle ~ .alectryon-output {
-    position: fixed;
-}
-
-@media screen and (min-width: 60rem) {
-    .alectryon-standalone .alectryon-windowed {
-        border-right-width: thin;
-        bottom: 0;
-        left: 0;
-        right: 50%;
-        top: 0;
-    }
-
-    .alectryon-standalone .alectryon-windowed .alectryon-sentence:hover .alectryon-output,
-    .alectryon-standalone .alectryon-windowed .alectryon-sentence.alectryon-target .alectryon-output {
-        bottom: 0;
-        left: 50%;
-        right: 0;
-        top: 0;
-    }
-}
-
-@media screen and (max-width: 60rem) {
-    .alectryon-standalone .alectryon-windowed {
-        border-bottom-width: 1px;
-        bottom: 40%;
-        left: 0;
-        right: 0;
-        top: 0;
-    }
-
-    .alectryon-standalone .alectryon-windowed .alectryon-sentence:hover .alectryon-output,
-    .alectryon-standalone .alectryon-windowed .alectryon-sentence.alectryon-target .alectryon-output {
-        bottom: 0;
-        left: 0;
-        right: 0;
-        top: 60%;
-    }
-}

static/alectryon/alectryon.js

@@ -1,172 +0,0 @@
-var Alectryon;
-(function(Alectryon) {
-    (function (slideshow) {
-        function anchor(sentence) { return "#" + sentence.id; }
-
-        function current_sentence() { return slideshow.sentences[slideshow.pos]; }
-
-        function unhighlight() {
-            var sentence = current_sentence();
-            if (sentence) sentence.classList.remove("alectryon-target");
-            slideshow.pos = -1;
-        }
-
-        function highlight(sentence) {
-            sentence.classList.add("alectryon-target");
-        }
-
-        function scroll(sentence) {
-            // Put the top of the current fragment close to the top of the
-            // screen, but scroll it out of view if showing it requires pushing
-            // the sentence past half of the screen.  If sentence is already in
-            // a reasonable position, don't move.
-            var parent = sentence.parentElement;
-            /* We want to scroll the whole document, so start at root… */
-            while (parent && !parent.classList.contains("alectryon-root"))
-                parent = parent.parentElement;
-            /* … and work up from there to find a scrollable element.
-               parent.scrollHeight can be greater than parent.clientHeight
-               without showing scrollbars, so we add a 10px buffer. */
-            while (parent && parent.scrollHeight <= parent.clientHeight + 10)
-                parent = parent.parentElement;
-            /* <body> and <html> elements can have their client rect overflow
-             * the window if their height is unset, so scroll the window
-             * instead */
-            if (parent && (parent.nodeName == "BODY" || parent.nodeName == "HTML"))
-                parent = null;
-
-            var rect = function(e) { return e.getBoundingClientRect(); };
-            var parent_box = parent ? rect(parent) : { y: 0, height: window.innerHeight },
-                sentence_y = rect(sentence).y - parent_box.y,
-                fragment_y = rect(sentence.parentElement).y - parent_box.y;
-
-            // The assertion below sometimes fails for the first element in a block.
-            // console.assert(sentence_y >= fragment_y);
-
-            if (sentence_y < 0.1 * parent_box.height ||
-                sentence_y > 0.7 * parent_box.height) {
-                (parent || window).scrollBy(
-                    0, Math.max(sentence_y - 0.5 * parent_box.height,
-                                fragment_y - 0.1 * parent_box.height));
-            }
-        }
-
-        function highlighted(pos) {
-            return slideshow.pos == pos;
-        }
-
-        function navigate(pos, inhibitScroll) {
-            unhighlight();
-            slideshow.pos = Math.min(Math.max(pos, 0), slideshow.sentences.length - 1);
-            var sentence = current_sentence();
-            highlight(sentence);
-            if (!inhibitScroll)
-                scroll(sentence);
-        }
-
-        var keys = {
-            PAGE_UP: 33,
-            PAGE_DOWN: 34,
-            ARROW_UP: 38,
-            ARROW_DOWN: 40,
-            h: 72, l: 76, p: 80, n: 78
-        };
-
-        function onkeydown(e) {
-            e = e || window.event;
-            if (e.ctrlKey || e.metaKey) {
-                if (e.keyCode == keys.ARROW_UP)
-                    slideshow.previous();
-                else if (e.keyCode == keys.ARROW_DOWN)
-                    slideshow.next();
-                else
-                    return;
-            } else {
-                // if (e.keyCode == keys.PAGE_UP || e.keyCode == keys.p || e.keyCode == keys.h)
-                //     slideshow.previous();
-                // else if (e.keyCode == keys.PAGE_DOWN || e.keyCode == keys.n || e.keyCode == keys.l)
-                //     slideshow.next();
-                // else
-                return;
-            }
-            e.preventDefault();
-        }
-
-        function start() {
-            slideshow.navigate(0);
-        }
-
-        function toggleHighlight(idx) {
-            if (highlighted(idx))
-                unhighlight();
-            else
-                navigate(idx, true);
-        }
-
-        function handleClick(evt) {
-            if (evt.ctrlKey || evt.metaKey) {
-                var sentence = evt.currentTarget;
-
-                // Ensure that the goal is shown on the side, not inline
-                var checkbox = sentence.getElementsByClassName("alectryon-toggle")[0];
-                if (checkbox)
-                    checkbox.checked = false;
-
-                toggleHighlight(sentence.alectryon_index);
-                evt.preventDefault();
-            }
-        }
-
-        function init() {
-            document.onkeydown = onkeydown;
-            slideshow.pos = -1;
-            slideshow.sentences = Array.from(document.getElementsByClassName("alectryon-sentence"));
-            slideshow.sentences.forEach(function (s, idx) {
-                s.addEventListener('click', handleClick, false);
-                s.alectryon_index = idx;
-            });
-        }
-
-        slideshow.start = start;
-        slideshow.end = unhighlight;
-        slideshow.navigate = navigate;
-        slideshow.next = function() { navigate(slideshow.pos + 1); };
-        slideshow.previous = function() { navigate(slideshow.pos + -1); };
-        window.addEventListener('DOMContentLoaded', init);
-    })(Alectryon.slideshow || (Alectryon.slideshow = {}));
-
-    (function (styles) {
-        var styleNames = ["centered", "floating", "windowed"];
-
-        function className(style) {
-            return "alectryon-" + style;
-        }
-
-        function setStyle(style) {
-            var root = document.getElementsByClassName("alectryon-root")[0];
-            styleNames.forEach(function (s) {
-                root.classList.remove(className(s)); });
-            root.classList.add(className(style));
-        }
-
-        function init() {
-            var banner = document.getElementsByClassName("alectryon-banner")[0];
-            if (banner) {
-                banner.append(" Style: ");
-                styleNames.forEach(function (styleName, idx) {
-                    var s = styleName;
-                    var a = document.createElement("a");
-                    a.onclick = function() { setStyle(s); };
-                    a.append(styleName);
-                    if (idx > 0) banner.append("; ");
-                    banner.appendChild(a);
-                });
-                banner.append(".");
-            }
-        }
-
-        window.addEventListener('DOMContentLoaded', init);
-
-        styles.setStyle = setStyle;
-    })(Alectryon.styles || (Alectryon.styles = {}));
-})(Alectryon || (Alectryon = {}));

static/alectryon/docutils_basic.css

@@ -1,593 +0,0 @@
-/******************************************************************************
-The MIT License (MIT)
-
-Copyright (c) 2014 Matthias Eisen
-Further changes Copyright (c) 2020, 2021 Clément Pit-Claudel
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in
-all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-THE SOFTWARE.
-******************************************************************************/
-
-kbd,
-pre,
-samp,
-tt,
-body code, /* Increase specificity to override IBM's stylesheet */
-body code.highlight,
-.docutils.literal {
-    font-family: 'Iosevka Slab Web', 'Iosevka Web', 'Iosevka Slab', 'Iosevka', 'Fira Code', monospace;
-    font-feature-settings: "COQX" 1 /* Coq ligatures */, "XV00" 1 /* Legacy */, "calt" 1 /* Fallback */;
-}
-
-body {
-    color: #111;
-    font-family: 'IBM Plex Serif', 'PT Serif', 'Merriweather', 'DejaVu Serif', serif;
-    line-height: 1.5;
-}
-
-main, div.document {
-    margin: 0 auto;
-    max-width: 720px;
-}
-
-
-/* ========== Headings ========== */
-
-h1, h2, h3, h4, h5, h6 {
-    font-weight: normal;
-    margin-top: 1.5em;
-}
-
-h1.section-subtitle, 
-h2.section-subtitle, 
-h3.section-subtitle,
-h4.section-subtitle, 
-h5.section-subtitle, 
-h6.section-subtitle {
-    margin-top: 0.4em;
-}
-
-h1.title {
-    text-align: center;
-}
-
-h2.subtitle {
-    text-align: center;
-}
-
-span.section-subtitle {
-    font-size: 80%,
-}
-
-/* //-------- Headings ---------- */
-
-
-/* ========== Images ========== */
-
-img, 
-.figure, 
-object {
-    display:        block;
-    margin-left:    auto;
-    margin-right:   auto;
-}
-
-div.figure {
-    margin-left:    2em;
-    margin-right:   2em;
-}
-
-img.align-left, .figure.align-left, object.align-left {
-    clear:          left;
-    float:          left;
-    margin-right:   1em;
-}
-
-img.align-right, .figure.align-right, object.align-right {
-    clear:          right;
-    float:          right;
-    margin-left:    1em;
-}
-
-img.align-center, .figure.align-center, object.align-center {
-    display:        block;
-    margin-left:    auto;
-    margin-right:   auto;
-}
-
-/* reset inner alignment in figures */
-div.align-right {
-    text-align: inherit;
-}
-
-object[type="image/svg+xml"], 
-object[type="application/x-shockwave-flash"] {
-    overflow: hidden;
-}
-
-/* //-------- Images ---------- */
-
-
-
-/* ========== Literal Blocks ========== */
-
-.docutils.literal {
-    background-color: #eee;
-    padding: 0 0.2em;
-    border-radius: 0.1em;
-}
-
-pre.address {
-    margin-bottom: 0;
-    margin-top: 0;
-    font: inherit;
-}
-
-pre.literal-block {
-    border-left: solid 5px #ccc;
-    padding: 1em; 
-}
-
-pre.literal-block, pre.doctest-block, pre.math, pre.code {
-}
-
-span.interpreted {
-}
-
-span.pre {
-    white-space: pre;
-}
-
-pre.code .ln { 
-    color: grey; 
-}
-pre.code, code {
-    border-style: none;
-    /* ! padding: 1em 0; */ /* Removed because that large hitbox bleeds over links on other lines */
-}
-pre.code .comment, code .comment { 
-    color: #888;
-}
-pre.code .keyword, code .keyword {
-    font-weight: bold; 
-    color: #080;
-}
-pre.code .literal.string, code .literal.string { 
-    color: #d20;
-    background-color: #fff0f0;
-}
-pre.code .literal.number, code .literal.number { 
-    color: #00d;
-}
-pre.code .name.builtin, code .name.builtin {
-    color: #038;
-    color: #820;
-}
-pre.code .name.namespace, code .name.namespace {
-    color: #b06;
-}
-pre.code .deleted, code .deleted {
-    background-color: #fdd;
-}
-pre.code .inserted, code .inserted {
-    background-color: #dfd;
-}
-
-
-/* //-------- Literal Blocks --------- */
-
-
-/* ========== Tables ========== */
-
-table {
-    border-spacing:         0;
-    border-collapse:        collapse;
-    border-style:           none;
-    border-top:             solid thin #111;
-    border-bottom:          solid thin #111;
-}
-
-td, 
-th {
-    border: none;
-    padding:                0.5em;
-    vertical-align:         top;
-}
-
-th {
-    border-top:             solid thin #111;
-    border-bottom:          solid thin #111;
-    background-color:       #ddd;
-}
-
-
-table.field-list,
-table.footnote,
-table.citation,
-table.option-list {
-    border:                 none;
-}
-table.docinfo {
-    margin:                 2em 4em;
-}
-
-table.docutils {
-    margin:                 1em 0;
-}
-
-table.docutils th.field-name, 
-table.docinfo th.docinfo-name {
-    border:                 none;
-    background:             none;
-    font-weight:            bold ;
-    text-align:             left ;
-    white-space:            nowrap ;
-    padding-left:           0;
-    vertical-align:         middle; 
-}
-
-table.docutils.booktabs {
-    border:                 none;
-    border-top:             medium solid;
-    border-bottom:          medium solid;
-    border-collapse:        collapse;
-}
-
-table.docutils.booktabs * {
-    border:                 none;
-}
-table.docutils.booktabs th {
-    border-bottom:          thin solid;
-    text-align:             left;
-}
-
-span.option {
-    white-space: nowrap;
-}
-
-table caption {
-    margin-bottom: 2px;
-}
-
-/* //-------- Tables ---------- */
-
-
-/* ========== Lists ========== */
-
-ol.simple, ul.simple {
-    margin-bottom: 1em;
-}
-
-ol.arabic {
-    list-style: decimal;
-}
-
-ol.loweralpha {
-    list-style: lower-alpha;
-}
-
-ol.upperalpha {
-    list-style: upper-alpha;
-}
-
-ol.lowerroman {
-    list-style: lower-roman;
-}
-
-ol.upperroman {
-    list-style: upper-roman;
-}
-
-dl.docutils dd {
-    margin-bottom: 0.5em;
-}
-
-
-dl.docutils dt {
-    font-weight: bold;
-}
-
-/* //-------- Lists ---------- */
-
-
-/* ========== Sidebar ========== */
-
-div.sidebar {
-    margin: 0 0 0.5em 1em ;
-    border-left: solid medium #111;
-    padding: 1em ;
-    width: 40% ;
-    float: right ;
-    clear: right;
-}
-
-div.sidebar {
-    font-size: 0.9rem;
-}
-
-p.sidebar-title {
-    font-size: 1rem;
-    font-weight: bold ;
-}
-
-p.sidebar-subtitle {
-    font-weight: bold;
-}
-
-/* //-------- Sidebar ---------- */
-
-
-/* ========== Topic ========== */
-
-div.topic {
-    border-left: thin solid #111;
-    padding-left: 1em;
-}
-
-div.topic p {
-    padding: 0;
-}
-
-p.topic-title {
-    font-weight: bold;
-}
-
-/* //-------- Topic ---------- */
-
-
-/* ========== Header ========== */
-
-div.header {
-    font-family:        "Century Gothic", CenturyGothic, Geneva, AppleGothic, sans-serif;
-    font-size:          0.9rem;
-    margin:             2em auto 4em auto;
-    max-width:          960px;
-    clear:              both;
-}
-
-hr.header {
-    border:             0;
-    height:             1px;
-    margin-top:         1em;
-    background-color:   #111;
-}
-
-/* //-------- Header ---------- */
-
-
-/* ========== Footer ========== */
-
-div.footer {
-    font-family:        "Century Gothic", CenturyGothic, Geneva, AppleGothic, sans-serif;
-    font-size:          0.9rem;
-    margin:             6em auto 2em auto;
-    max-width:          960px;
-    clear:              both;
-    text-align:         center;
-}
-
-hr.footer {
-    border:             0;
-    height:             1px;
-    margin-bottom:      2em;
-    background-color:   #111;
-}
-
-/* //-------- Footer ---------- */
-
-
-/* ========== Admonitions ========== */
-
-div.admonition, 
-div.attention, 
-div.caution, 
-div.danger, 
-div.error,
-div.hint, 
-div.important, 
-div.note, 
-div.tip, 
-div.warning {
-    border: solid thin #111;
-    padding: 0 1em;
-}
-
-div.error,
-div.danger {
-    border-color: #a94442;
-    background-color: #f2dede;
-}
-
-div.hint,
-div.tip {
-    border-color: #31708f;
-    background-color: #d9edf7;
-}
-
-div.attention,
-div.caution,
-div.warning {
-    border-color: #8a6d3b;
-    background-color: #fcf8e3; 
-}
-
-div.hint p.admonition-title,
-div.tip p.admonition-title {
-    color: #31708f;
-    font-weight: bold ;
-}
-
-div.note p.admonition-title,
-div.admonition p.admonition-title, 
-div.important p.admonition-title {
-    font-weight: bold ;
-}
-
-div.attention p.admonition-title,
-div.caution p.admonition-title,
-div.warning p.admonition-title {
-    color: #8a6d3b;
-    font-weight: bold ;
-}
-
-div.danger p.admonition-title, 
-div.error p.admonition-title,
-.code .error {
-    color: #a94442;
-    font-weight: bold ;
-}
-
-/* //-------- Admonitions ---------- */
-
-
-/* ========== Table of Contents ========== */
-
-div.contents {
-    margin: 2em 0;
-    border: none;
-}
-
-ul.auto-toc {
-    list-style-type: none;
-}
-
-a.toc-backref {
-    text-decoration: none ;
-    color: #111;
-}
-
-/* //-------- Table of Contents ---------- */
-
-
-
-/* ========== Line Blocks========== */
-
-div.line-block {
-    display: block ;
-    margin-top: 1em ;
-    margin-bottom: 1em;
-}
-
-div.line-block div.line-block {
-    margin-top: 0 ;
-    margin-bottom: 0 ;
-    margin-left: 1.5em;
-}
-
-/* //-------- Line Blocks---------- */
-
-
-/* ========== System Messages ========== */
-
-div.system-messages {
-    margin: 5em;
-}
-
-div.system-messages h1 {
-    color: red;
-}
-
-div.system-message {
-    border: medium outset ;
-    padding: 1em;
-}
-
-div.system-message p.system-message-title {
-    color: red ;
-    font-weight: bold;
-}
-
-/* //-------- System Messages---------- */
-
-
-/* ========== Helpers ========== */
-
-.hidden {
-    display: none;
-}
-
-.align-left {
-    text-align: left;
-}
-
-.align-center {
-    clear: both ;
-    text-align: center;
-}
-
-.align-right {
-    text-align: right;
-}
-
-/* //-------- Helpers---------- */
-
-
-p.caption {
-    font-style: italic;
-    text-align: center;
-}
-
-p.credits {
-font-style: italic ;
-font-size: smaller }
-
-p.label {
-white-space: nowrap }
-
-p.rubric {
-font-weight: bold ;
-font-size: larger ;
-color: maroon ;
-text-align: center }
-
-p.attribution {
-text-align: right ;
-margin-left: 50% }
-
-blockquote.epigraph {
-    margin: 2em 5em;
-}
-
-div.abstract {
-margin: 2em 5em }
-
-div.abstract {
-font-weight: bold ;
-text-align: center }
-
-div.dedication {
-margin: 2em 5em ;
-text-align: center ;
-font-style: italic }
-
-div.dedication {
-font-weight: bold ;
-font-style: normal }
-
-
-span.classifier {
-font-style: oblique }
-
-span.classifier-delimiter {
-font-weight: bold }
-
-span.problematic {
-color: red }
-
-
-

static/alectryon/pygments.css

@@ -1,82 +0,0 @@
-/* Pygments stylesheet generated by Alectryon (style=None) */
-/* Most of the following are unused as of now */
-td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
-span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
-td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
-span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
-.highlight .hll, .code .hll { background-color: #ffffcc }
-.highlight .c, .code .c { color: #555753; font-style: italic } /* Comment */
-.highlight .err, .code .err { color: #a40000; border: 1px solid #cc0000 } /* Error */
-.highlight .g, .code .g { color: #000000 } /* Generic */
-.highlight .k, .code .k { color: #8f5902 } /* Keyword */
-.highlight .l, .code .l { color: #2e3436 } /* Literal */
-.highlight .n, .code .n { color: #000000 } /* Name */
-.highlight .o, .code .o { color: #000000 } /* Operator */
-.highlight .x, .code .x { color: #2e3436 } /* Other */
-.highlight .p, .code .p { color: #000000 } /* Punctuation */
-.highlight .ch, .code .ch { color: #555753; font-weight: bold; font-style: italic } /* Comment.Hashbang */
-.highlight .cm, .code .cm { color: #555753; font-style: italic } /* Comment.Multiline */
-.highlight .cp, .code .cp { color: #3465a4; font-style: italic } /* Comment.Preproc */
-.highlight .cpf, .code .cpf { color: #555753; font-style: italic } /* Comment.PreprocFile */
-.highlight .c1, .code .c1 { color: #555753; font-style: italic } /* Comment.Single */
-.highlight .cs, .code .cs { color: #3465a4; font-weight: bold; font-style: italic } /* Comment.Special */
-.highlight .gd, .code .gd { color: #a40000 } /* Generic.Deleted */
-.highlight .ge, .code .ge { color: #000000; font-style: italic } /* Generic.Emph */
-.highlight .gr, .code .gr { color: #a40000 } /* Generic.Error */
-.highlight .gh, .code .gh { color: #a40000; font-weight: bold } /* Generic.Heading */
-.highlight .gi, .code .gi { color: #4e9a06 } /* Generic.Inserted */
-.highlight .go, .code .go { color: #000000; font-style: italic } /* Generic.Output */
-.highlight .gp, .code .gp { color: #8f5902 } /* Generic.Prompt */
-.highlight .gs, .code .gs { color: #000000; font-weight: bold } /* Generic.Strong */
-.highlight .gu, .code .gu { color: #000000; font-weight: bold } /* Generic.Subheading */
-.highlight .gt, .code .gt { color: #000000; font-style: italic } /* Generic.Traceback */
-.highlight .kc, .code .kc { color: #204a87; font-weight: bold } /* Keyword.Constant */
-.highlight .kd, .code .kd { color: #4e9a06; font-weight: bold } /* Keyword.Declaration */
-.highlight .kn, .code .kn { color: #4e9a06; font-weight: bold } /* Keyword.Namespace */
-.highlight .kp, .code .kp { color: #204a87 } /* Keyword.Pseudo */
-.highlight .kr, .code .kr { color: #8f5902 } /* Keyword.Reserved */
-.highlight .kt, .code .kt { color: #204a87 } /* Keyword.Type */
-.highlight .ld, .code .ld { color: #2e3436 } /* Literal.Date */
-.highlight .m, .code .m { color: #2e3436 } /* Literal.Number */
-.highlight .s, .code .s { color: #ad7fa8 } /* Literal.String */
-.highlight .na, .code .na { color: #c4a000 } /* Name.Attribute */
-.highlight .nb, .code .nb { color: #75507b } /* Name.Builtin */
-.highlight .nc, .code .nc { color: #204a87 } /* Name.Class */
-.highlight .no, .code .no { color: #ce5c00 } /* Name.Constant */
-.highlight .nd, .code .nd { color: #3465a4; font-weight: bold } /* Name.Decorator */
-.highlight .ni, .code .ni { color: #c4a000; text-decoration: underline } /* Name.Entity */
-.highlight .ne, .code .ne { color: #cc0000 } /* Name.Exception */
-.highlight .nf, .code .nf { color: #a40000 } /* Name.Function */
-.highlight .nl, .code .nl { color: #3465a4; font-weight: bold } /* Name.Label */
-.highlight .nn, .code .nn { color: #000000 } /* Name.Namespace */
-.highlight .nx, .code .nx { color: #000000 } /* Name.Other */
-.highlight .py, .code .py { color: #000000 } /* Name.Property */
-.highlight .nt, .code .nt { color: #a40000 } /* Name.Tag */
-.highlight .nv, .code .nv { color: #ce5c00 } /* Name.Variable */
-.highlight .ow, .code .ow { color: #8f5902 } /* Operator.Word */
-.highlight .w, .code .w { color: #d3d7cf; text-decoration: underline } /* Text.Whitespace */
-.highlight .mb, .code .mb { color: #2e3436 } /* Literal.Number.Bin */
-.highlight .mf, .code .mf { color: #2e3436 } /* Literal.Number.Float */
-.highlight .mh, .code .mh { color: #2e3436 } /* Literal.Number.Hex */
-.highlight .mi, .code .mi { color: #2e3436 } /* Literal.Number.Integer */
-.highlight .mo, .code .mo { color: #2e3436 } /* Literal.Number.Oct */
-.highlight .sa, .code .sa { color: #ad7fa8 } /* Literal.String.Affix */
-.highlight .sb, .code .sb { color: #ad7fa8 } /* Literal.String.Backtick */
-.highlight .sc, .code .sc { color: #ad7fa8; font-weight: bold } /* Literal.String.Char */
-.highlight .dl, .code .dl { color: #ad7fa8 } /* Literal.String.Delimiter */
-.highlight .sd, .code .sd { color: #ad7fa8 } /* Literal.String.Doc */
-.highlight .s2, .code .s2 { color: #ad7fa8 } /* Literal.String.Double */
-.highlight .se, .code .se { color: #ad7fa8; font-weight: bold } /* Literal.String.Escape */
-.highlight .sh, .code .sh { color: #ad7fa8; text-decoration: underline } /* Literal.String.Heredoc */
-.highlight .si, .code .si { color: #ce5c00 } /* Literal.String.Interpol */
-.highlight .sx, .code .sx { color: #ad7fa8 } /* Literal.String.Other */
-.highlight .sr, .code .sr { color: #ad7fa8 } /* Literal.String.Regex */
-.highlight .s1, .code .s1 { color: #ad7fa8 } /* Literal.String.Single */
-.highlight .ss, .code .ss { color: #8f5902 } /* Literal.String.Symbol */
-.highlight .bp, .code .bp { color: #5c35cc } /* Name.Builtin.Pseudo */
-.highlight .fm, .code .fm { color: #a40000 } /* Name.Function.Magic */
-.highlight .vc, .code .vc { color: #ce5c00 } /* Name.Variable.Class */
-.highlight .vg, .code .vg { color: #ce5c00; text-decoration: underline } /* Name.Variable.Global */
-.highlight .vi, .code .vi { color: #ce5c00 } /* Name.Variable.Instance */
-.highlight .vm, .code .vm { color: #ce5c00 } /* Name.Variable.Magic */
-.highlight .il, .code .il { color: #2e3436 } /* Literal.Number.Integer.Long */

static/color-scheme.js

@@ -1,33 +0,0 @@
-function getTheme() {
-    return localStorage.getItem("theme") || "system";
-}
-
-function setTheme(themeName) {
-    localStorage.setItem('theme', themeName);
-    if (themeName == "system") {
-        themeName = parent.matchMedia("(prefers-color-scheme: dark)").matches ? "dark" : "light";
-    }
-    // the navbar is in an iframe, so we need to set this variable in the parent document
-    for (const win of [window, parent]) {
-        win.document.documentElement.setAttribute('data-theme', themeName);
-    }
-}
-
-setTheme(getTheme())
-
-document.addEventListener("DOMContentLoaded", function() {
-    document.querySelectorAll("#color-theme-switcher input").forEach((input) => {
-        if (input.value == getTheme()) {
-            input.checked = true;
-        }
-        input.addEventListener('change', e => setTheme(e.target.value));
-    });
-
-    // also check to see if the user changes their theme settings while the page is loaded.
-    parent.matchMedia('(prefers-color-scheme: dark)').addEventListener('change', event => {
-        setTheme(getTheme());
-    })
-});
-
-// un-hide the colorscheme picker
-document.querySelector("#settings").removeAttribute('hidden');

static/declaration-data.js

@@ -1,287 +0,0 @@
-/**
- * This module is a wrapper that facilitates manipulating the declaration data.
- *
- * Please see {@link DeclarationDataCenter} for more information.
- */
-
-const CACHE_DB_NAME = "declaration-data";
-const CACHE_DB_VERSION = 1;
-const CACHE_DB_KEY = "DECLARATIONS_KEY";
-
-/**
- * The DeclarationDataCenter is used for declaration searching.
- *
- * For usage, see the {@link init} and {@link search} methods.
- */
-export class DeclarationDataCenter {
-  /**
-   * The declaration data. Users should not interact directly with this field.
-   *
-   * *NOTE:* This is not made private to support legacy browsers.
-   */
-  declarationData = null;
-
-  /**
-   * Used to implement the singleton, in case we need to fetch data mutiple times in the same page.
-   */
-  static requestSingleton = null;
-
-  /**
-   * Construct a DeclarationDataCenter with given data.
-   *
-   * Please use {@link DeclarationDataCenter.init} instead, which automates the data fetching process.
-   * @param {*} declarationData
-   */
-  constructor(declarationData) {
-    this.declarationData = declarationData;
-  }
-
-  /**
-   * The actual constructor of DeclarationDataCenter
-   * @returns {Promise<DeclarationDataCenter>}
-   */
-  static async init() {
-    if (DeclarationDataCenter.requestSingleton === null) {
-      DeclarationDataCenter.requestSingleton = DeclarationDataCenter.getData();
-    }
-    return await DeclarationDataCenter.requestSingleton;
-  }
-
-  static async getData() {
-    const dataListUrl = new URL(
-      `${SITE_ROOT}/declarations/declaration-data.bmp`,
-      window.location
-    );
-
-    // try to use cache first
-    const data = await fetchCachedDeclarationData().catch(_e => null);
-    if (data) {
-      // if data is defined, use the cached one.
-      return new DeclarationDataCenter(data);
-    } else {
-      // undefined. then fetch the data from the server.
-      const dataListRes = await fetch(dataListUrl);
-      const data = await dataListRes.json();
-      // TODO https://github.com/leanprover/doc-gen4/issues/133
-      // await cacheDeclarationData(data);
-      return new DeclarationDataCenter(data);
-    }
-  }
-
-  /**
-   * Search for a declaration.
-   * @returns {Array<any>}
-   */
-  search(pattern, strict = true, allowedKinds=undefined, maxResults=undefined) {
-    if (!pattern) {
-      return [];
-    }
-    if (strict) {
-      let decl = this.declarationData.declarations[pattern];
-      return decl ? [decl] : [];
-    } else {
-      return getMatches(this.declarationData.declarations, pattern, allowedKinds, maxResults);
-    }
-  }
-
-  /**
-   * Search for all instances of a certain typeclass
-   * @returns {Array<String>}
-   */
-  instancesForClass(className) {
-    const instances = this.declarationData.instances[className];
-    if (!instances) {
-      return [];
-    } else {
-      return instances;
-    }
-  }
-
-  /**
-   * Search for all instances that involve a certain type
-   * @returns {Array<String>}
-   */
-  instancesForType(typeName) {
-    const instances = this.declarationData.instancesFor[typeName];
-    if (!instances) {
-      return [];
-    } else {
-      return instances;
-    }
-  }
-
-  /**
-   * Analogous to Lean declNameToLink
-   * @returns {String}
-   */
-  declNameToLink(declName) {
-    return this.declarationData.declarations[declName].docLink;
-  }
-
-  /**
-   * Find all modules that imported the given one.
-   * @returns {Array<String>}
-   */
-  moduleImportedBy(moduleName) {
-    return this.declarationData.importedBy[moduleName];
-  }
-
-  /**
-   * Analogous to Lean moduleNameToLink
-   * @returns {String}
-   */
-  moduleNameToLink(moduleName) {
-    return this.declarationData.modules[moduleName];
-  }
-}
-
-function isSeparater(char) {
-  return char === "." || char === "_";
-}
-
-// HACK: the fuzzy matching is quite hacky
-
-function matchCaseSensitive(declName, lowerDeclName, pattern) {
-  let i = 0,
-    j = 0,
-    err = 0,
-    lastMatch = 0;
-  while (i < declName.length && j < pattern.length) {
-    if (pattern[j] === declName[i] || pattern[j] === lowerDeclName[i]) {
-      err += (isSeparater(pattern[j]) ? 0.125 : 1) * (i - lastMatch);
-      if (pattern[j] !== declName[i]) err += 0.5;
-      lastMatch = i + 1;
-      j++;
-    } else if (isSeparater(declName[i])) {
-      err += 0.125 * (i + 1 - lastMatch);
-      lastMatch = i + 1;
-    }
-    i++;
-  }
-  err += 0.125 * (declName.length - lastMatch);
-  if (j === pattern.length) {
-    return err;
-  }
-}
-
-function getMatches(declarations, pattern, allowedKinds = undefined, maxResults = undefined) {
-  const lowerPats = pattern.toLowerCase().split(/\s/g);
-  const patNoSpaces = pattern.replace(/\s/g, "");
-  const results = [];
-  for (const [_, {
-    name,
-    kind,
-    doc,
-    docLink,
-    sourceLink,
-  }] of Object.entries(declarations)) {
-    // Apply "kind" filter
-    if (allowedKinds !== undefined) {
-      if (!allowedKinds.has(kind)) {
-        continue;
-      }
-    }
-    const lowerName = name.toLowerCase();
-    const lowerDoc = doc.toLowerCase();
-    let err = matchCaseSensitive(name, lowerName, patNoSpaces);
-    // match all words as substrings of docstring
-    if (
-      err >= 3 &&
-      pattern.length > 3 &&
-      lowerPats.every((l) => lowerDoc.indexOf(l) != -1)
-    ) {
-      err = 3;
-    }
-    if (err !== undefined) {
-      results.push({
-        name,
-        kind,
-        doc,
-        err,
-        lowerName,
-        lowerDoc,
-        docLink,
-        sourceLink,
-      });
-    }
-  }
-  return results.sort(({ err: a }, { err: b }) => a - b).slice(0, maxResults);
-}
-
-// TODO: refactor the indexedDB part to be more robust
-
-/**
- * Get the indexedDB database, automatically initialized.
- * @returns {Promise<IDBDatabase>}
- */
-async function getDeclarationDatabase() {
-  return new Promise((resolve, reject) => {
-    const request = indexedDB.open(CACHE_DB_NAME, CACHE_DB_VERSION);
-
-    request.onerror = function (event) {
-      reject(
-        new Error(
-          `fail to open indexedDB ${CACHE_DB_NAME} of version ${CACHE_DB_VERSION}`
-        )
-      );
-    };
-    request.onupgradeneeded = function (event) {
-      let db = event.target.result;
-      // We only need to store one object, so no key path or increment is needed.
-      db.createObjectStore("declaration");
-    };
-    request.onsuccess = function (event) {
-      resolve(event.target.result);
-    };
-  });
-}
-
-/**
- * Store data in indexedDB object store.
- * @param {Map<string, any>} data
- */
-async function cacheDeclarationData(data) {
-  let db = await getDeclarationDatabase();
-  let store = db
-    .transaction("declaration", "readwrite")
-    .objectStore("declaration");
-  return new Promise((resolve, reject) => {
-    let clearRequest = store.clear();
-    let addRequest = store.add(data, CACHE_DB_KEY);
-
-    addRequest.onsuccess = function (event) {
-      resolve();
-    };
-    addRequest.onerror = function (event) {
-      reject(new Error(`fail to store declaration data`));
-    };
-    clearRequest.onerror = function (event) {
-      reject(new Error("fail to clear object store"));
-    };
-  });
-}
-
-/**
- * Retrieve data from indexedDB database.
- * @returns {Promise<Map<string, any>|undefined>}
- */
-async function fetchCachedDeclarationData() {
-  let db = await getDeclarationDatabase();
-  let store = db
-    .transaction("declaration", "readonly")
-    .objectStore("declaration");
-  return new Promise((resolve, reject) => {
-    let transactionRequest = store.get(CACHE_DB_KEY);
-    transactionRequest.onsuccess = function (event) {
-      // TODO: This API is not thought 100% through. If we have a DB cached
-      // already it will not even ask the remote for a new one so we end up
-      // with outdated declaration-data. This has to have some form of cache
-      // invalidation: https://github.com/leanprover/doc-gen4/issues/133
-      // resolve(event.target.result);
-      resolve(undefined);
-    };
-    transactionRequest.onerror = function (event) {
-      reject(new Error(`fail to store declaration data`));
-    };
-  });
-}

static/find/find.js

@@ -1,93 +0,0 @@
-/**
- * This module is used for the `/find` endpoint.
- *
- * Two basic kinds of search syntax are supported:
- *
- * 1. Query-Fragment syntax: `/find?pattern=Nat.add#doc` for documentation and `/find?pattern=Nat.add#src` for source code.
- * 2. Fragment-Only syntax:`/find/#doc/Nat.add` for documentation and `/find/#src/Nat.add` for source code.
- *
- * Though both of them are valid, the first one is highly recommended, and the second one is for compatibility and taste.
- *
- * There are some extended usage for the QF syntax. For example, appending `strict=false` to the query part
- * (`/find?pattern=Nat.add&strict=false#doc`) will allow you to use the fuzzy search, rather than strict match.
- * Also, the fragment is extensible as well. For now only `#doc` and `#src` are implement, and the plain query without
- * hash (`/find?pattern=Nat.add`) is used for computer-friendly data (semantic web is great! :P), while all other fragments
- * fallback to the `#doc` view.
- */
-
-import { DeclarationDataCenter } from "../declaration-data.js";
-
-function leanFriendlyRegExp(c) {
-  try {
-    return new RegExp("(?<!«[^»]*)" + c);
-  } catch (e) {
-    if (e instanceof SyntaxError) {
-      // Lookbehind is not implemented yet in WebKit: https://bugs.webkit.org/show_bug.cgi?id=174931
-      // Fall back to less friendly regex.
-      return new RegExp(c);
-    }
-    throw e;
-  }
-}
-
-/**
- * We don't use browser's default hash and searchParams in case Lean declaration name
- * can be like `«#»`, rather we manually handle the `window.location.href` with regex.
- */
-const LEAN_FRIENDLY_URL_REGEX = /^[^?#]+(?:\?((?:[^«#»]|«.*»)*))?(?:#(.*))?$/;
-const LEAN_FRIENDLY_AND_SEPARATOR = leanFriendlyRegExp("&");
-const LEAN_FRIENDLY_EQUAL_SEPARATOR = leanFriendlyRegExp("=");
-const LEAN_FRIENDLY_SLASH_SEPARATOR = leanFriendlyRegExp("/");
-
-const [_, query, fragment] = LEAN_FRIENDLY_URL_REGEX.exec(window.location.href);
-const queryParams = new Map(
-  query
-    ?.split(LEAN_FRIENDLY_AND_SEPARATOR)
-    ?.map((p) => p.split(LEAN_FRIENDLY_EQUAL_SEPARATOR))
-    ?.filter((l) => l.length == 2 && l[0].length > 0)
-);
-const fragmentPaths = fragment?.split(LEAN_FRIENDLY_SLASH_SEPARATOR) ?? [];
-
-const encodedPattern = queryParams.get("pattern") ?? fragmentPaths[1]; // if first fail then second, may be undefined
-const pattern = decodeURIComponent(encodedPattern);
-const strict = (queryParams.get("strict") ?? "true") === "true"; // default to true
-const view = fragmentPaths[0];
-
-findAndRedirect(pattern, strict, view);
-
-/**
- * Find the result and redirect to the result page.
- * @param {string} pattern the pattern to search for
- * @param {string} view the view of the find result (`"doc"` or `"src"` for now)
- */
-async function findAndRedirect(pattern, strict, view) {
-  // if no pattern provided, directly redirect to the 404 page
-  if (!pattern) {
-    window.location.replace(`${SITE_ROOT}404.html`);
-  }
-  // search for result
-  try {
-    const dataCenter = await DeclarationDataCenter.init();
-    let result = (dataCenter.search(pattern, strict) ?? [])[0]; // in case return non array
-    // if no result found, redirect to the 404 page
-    if (!result) {
-      // TODO: better url semantic for 404, current implementation will lead to duplicate search for fuzzy match if not found.
-      window.location.replace(`${SITE_ROOT}404.html#${pattern ?? ""}`);
-    } else {
-      result.docLink = SITE_ROOT + result.docLink;
-      // success, redirect to doc or source page, or to the semantic rdf.
-      if (!view) {
-        window.location.replace(result.link);
-      } else if (view == "doc") {
-        window.location.replace(result.docLink);
-      } else if (view == "src") {
-        window.location.replace(result.sourceLink);
-      } else {
-        // fallback to doc page
-        window.location.replace(result.docLink);
-      }
-    }
-  } catch (e) {
-    document.write(`Cannot fetch data, please check your network connection.\n${e}`);
-  }
-}

static/how-about.js

@@ -1,39 +0,0 @@
-/**
- * This module implements the `howabout` functionality in the 404 page.
- */
-
-import { DeclarationDataCenter } from "./declaration-data.js";
-
-const HOW_ABOUT = document.querySelector("#howabout");
-
-// Show url of the missing page
-if (HOW_ABOUT) {
-  HOW_ABOUT.parentNode
-    .insertBefore(document.createElement("pre"), HOW_ABOUT)
-    .appendChild(document.createElement("code")).innerText =
-    window.location.href.replace(/[/]/g, "/\u200b");
-
-  // TODO: add how about functionality for similar page as well.
-  const pattern = window.location.hash.replace("#", "");
-
-  // try to search for similar declarations
-  if (pattern) {
-    HOW_ABOUT.innerText = "Please wait a second. I'll try to help you.";
-    DeclarationDataCenter.init().then((dataCenter) => {
-      let results = dataCenter.search(pattern, false);
-      if (results.length > 0) {
-        HOW_ABOUT.innerText = "How about one of these instead:";
-        const ul = HOW_ABOUT.appendChild(document.createElement("ul"));
-        for (const { name, docLink } of results) {
-          const li = ul.appendChild(document.createElement("li"));
-          const a = li.appendChild(document.createElement("a"));
-          a.href = docLink;
-          a.appendChild(document.createElement("code")).innerText = name;
-        }
-      } else {
-        HOW_ABOUT.innerText =
-          "Sorry, I cannot find any similar declarations. Check the link or use the module navigation to find what you want :P";
-      }
-    });
-  }
-}

static/importedBy.js

@@ -1,19 +0,0 @@
-import { DeclarationDataCenter } from "./declaration-data.js";
-
-fillImportedBy();
-
-async function fillImportedBy() {
-  if (!MODULE_NAME) {
-    return;
-  }
-  const dataCenter = await DeclarationDataCenter.init();
-  const moduleName = MODULE_NAME;
-  const importedByList = document.querySelector(".imported-by-list");
-  const importedBy = dataCenter.moduleImportedBy(moduleName);
-  var innerHTML = "";
-  for(var module of importedBy) {
-    const moduleLink = dataCenter.moduleNameToLink(module);
-    innerHTML += `<li><a href="${SITE_ROOT}${moduleLink}">${module}</a></li>`
-  }
-  importedByList.innerHTML = innerHTML;
-}

static/instances.js

@@ -1,36 +0,0 @@
-import { DeclarationDataCenter } from "./declaration-data.js";
-
-annotateInstances();
-annotateInstancesFor()
-
-async function annotateInstances() {
-  const dataCenter = await DeclarationDataCenter.init();
-  const instanceForLists = [...(document.querySelectorAll(".instances-list"))];
-
-  for (const instanceForList of instanceForLists) {
-    const className = instanceForList.id.slice("instances-list-".length);
-    const instances = dataCenter.instancesForClass(className);
-    var innerHTML = "";
-    for(var instance of instances) {
-      const instanceLink = dataCenter.declNameToLink(instance);
-      innerHTML += `<li><a href="${SITE_ROOT}${instanceLink}">${instance}</a></li>`
-    }
-    instanceForList.innerHTML = innerHTML;
-  }
-}
-
-async function annotateInstancesFor() {
-  const dataCenter = await DeclarationDataCenter.init();
-  const instanceForLists = [...(document.querySelectorAll(".instances-for-list"))];
-
-  for (const instanceForList of instanceForLists) {
-    const typeName = instanceForList.id.slice("instances-for-list-".length);
-    const instances = dataCenter.instancesForType(typeName);
-    var innerHTML = "";
-    for(var instance of instances) {
-      const instanceLink = dataCenter.declNameToLink(instance);
-      innerHTML += `<li><a href="${SITE_ROOT}${instanceLink}">${instance}</a></li>`
-    }
-    instanceForList.innerHTML = innerHTML;
-  }
-}

static/mathjax-config.js

@@ -1,41 +0,0 @@
-/*
- * This file is for configing MathJax behavior.
- * See https://docs.mathjax.org/en/latest/web/configuration.html
- * 
- * This configuration is copied from old doc-gen3
- * https://github.com/leanprover-community/doc-gen
- */
-MathJax = {
-  tex: {
-    inlineMath: [["$", "$"]],
-    displayMath: [["$$", "$$"]],
-  },
-  options: {
-    skipHtmlTags: [
-      "script",
-      "noscript",
-      "style",
-      "textarea",
-      "pre",
-      "code",
-      "annotation",
-      "annotation-xml",
-      "decl",
-      "decl_meta",
-      "attributes",
-      "decl_args",
-      "decl_header",
-      "decl_name",
-      "decl_type",
-      "equation",
-      "equations",
-      "structure_field",
-      "structure_fields",
-      "constructor",
-      "constructors",
-      "instances",
-    ],
-    ignoreHtmlClass: "tex2jax_ignore",
-    processHtmlClass: "tex2jax_process",
-  },
-};

static/nav.js

@@ -1,43 +0,0 @@
-/**
- * This module is used to implement persistent navbar expansion.
- */
-
-// The variable to store the expansion information.
-let expanded = {};
-
-// Load expansion information from sessionStorage.
-for (const e of (sessionStorage.getItem("expanded") || "").split(",")) {
-  if (e !== "") {
-    expanded[e] = true;
-  }
-}
-
-/**
- * Save expansion information to sessionStorage.
- */
-function saveExpanded() {
-  sessionStorage.setItem(
-    "expanded",
-    Object.getOwnPropertyNames(expanded)
-      .filter((e) => expanded[e])
-      .join(",")
-  );
-}
-
-// save expansion information when user change the expansion.
-for (const elem of document.getElementsByClassName("nav_sect")) {
-  const id = elem.getAttribute("data-path");
-  if (!id) continue;
-  if (expanded[id]) {
-    elem.open = true;
-  }
-  elem.addEventListener("toggle", () => {
-    expanded[id] = elem.open;
-    saveExpanded();
-  });
-}
-
-// Scroll to center.
-for (const currentFileLink of document.getElementsByClassName("visible")) {
-  currentFileLink.scrollIntoView({ block: "center" });
-}

static/search.js

@@ -1,158 +0,0 @@
-/**
- * This module is used to handle user's interaction with the search form.
- */
-
-import { DeclarationDataCenter } from "./declaration-data.js";
-
-// Search form and input in the upper right toolbar
-const SEARCH_FORM = document.querySelector("#search_form");
-const SEARCH_INPUT = SEARCH_FORM.querySelector("input[name=q]");
-
-// Search form on the /search.html_page.  These may be null.
-const SEARCH_PAGE_INPUT = document.querySelector("#search_page_query")
-const SEARCH_RESULTS = document.querySelector("#search_results")
-
-// Max results to show for autocomplete or /search.html page.
-const AC_MAX_RESULTS = 30
-const SEARCH_PAGE_MAX_RESULTS = undefined
-
-// Create an `div#autocomplete_results` to hold all autocomplete results.
-let ac_results = document.createElement("div");
-ac_results.id = "autocomplete_results";
-SEARCH_FORM.appendChild(ac_results);
-
-/**
- * Attach `selected` class to the the selected autocomplete result.
- */
-function handleSearchCursorUpDown(down) {
-  const sel = ac_results.querySelector(`.selected`);
-  if (sel) {
-    sel.classList.remove("selected");
-    const toSelect = down
-      ? sel.nextSibling 
-      : sel.previousSibling;
-    toSelect && toSelect.classList.add("selected");
-  } else {
-    const toSelect = down ? ac_results.firstChild : ac_results.lastChild;
-    toSelect && toSelect.classList.add("selected");
-  }
-}
-
-/**
- * Perform search (when enter is pressed).
- */
-function handleSearchEnter() {
-  const sel = ac_results.querySelector(`.selected .result_link a`) || document.querySelector(`#search_button`);
-  sel.click();
-}
-
-/**
- * Allow user to navigate autocomplete results with up/down arrow keys, and choose with enter.
- */
-SEARCH_INPUT.addEventListener("keydown", (ev) => {
-  switch (ev.key) {
-    case "Down":
-    case "ArrowDown":
-      ev.preventDefault();
-      handleSearchCursorUpDown(true);
-      break;
-    case "Up":
-    case "ArrowUp":
-      ev.preventDefault();
-      handleSearchCursorUpDown(false);
-      break;
-    case "Enter":
-      ev.preventDefault();
-      handleSearchEnter();
-      break;
-  }
-});
-
-/**
- * Remove all children of a DOM node.
- */
-function removeAllChildren(node) {
-  while (node.firstChild) {
-    node.removeChild(node.lastChild);
-  }
-}
-
-/**
- * Handle user input and perform search.
- */
-function handleSearch(dataCenter, err, ev, sr, maxResults, autocomplete) {
-  const text = ev.target.value;
-
-  // If no input clear all.
-  if (!text) {
-    sr.removeAttribute("state");
-    removeAllChildren(sr);
-    return;
-  }
-
-  // searching
-  sr.setAttribute("state", "loading");
-
-  if (dataCenter) {
-    var allowedKinds;
-    if (!autocomplete) {
-      allowedKinds = new Set();
-      document.querySelectorAll(".kind_checkbox").forEach((checkbox) =>
-        {
-          if (checkbox.checked) {
-            allowedKinds.add(checkbox.value);
-          }
-        } 
-      );
-    }
-    const result = dataCenter.search(text, false, allowedKinds, maxResults);
-
-    // in case user has updated the input.
-    if (ev.target.value != text) return;
-  
-    // update autocomplete results
-    removeAllChildren(sr);
-    for (const { name, kind, doc, docLink } of result) {
-      const row = sr.appendChild(document.createElement("div"));
-      row.classList.add("search_result")
-      const linkdiv = row.appendChild(document.createElement("div"))
-      linkdiv.classList.add("result_link")
-      const link = linkdiv.appendChild(document.createElement("a"));
-      link.innerText = name;
-      link.title = name;
-      link.href = SITE_ROOT + docLink;
-      if (!autocomplete) {
-        const doctext = row.appendChild(document.createElement("div"));
-        doctext.innerText = doc
-        doctext.classList.add("result_doc")
-      }
-    }
-  }
-  // handle error
-  else {
-    removeAllChildren(sr);
-    const d = sr.appendChild(document.createElement("a"));
-    d.innerText = `Cannot fetch data, please check your network connection.\n${err}`;
-  }
-  sr.setAttribute("state", "done");
-}
-
-DeclarationDataCenter.init()
-  .then((dataCenter) => {
-    // Search autocompletion.
-    SEARCH_INPUT.addEventListener("input", ev => handleSearch(dataCenter, null, ev, ac_results, AC_MAX_RESULTS, true));
-    if(SEARCH_PAGE_INPUT) {
-      SEARCH_PAGE_INPUT.addEventListener("input", ev => handleSearch(dataCenter, null, ev, SEARCH_RESULTS, SEARCH_PAGE_MAX_RESULTS, false))
-      document.querySelectorAll(".kind_checkbox").forEach((checkbox) =>
-        checkbox.addEventListener("input", ev => SEARCH_PAGE_INPUT.dispatchEvent(new Event("input")))
-      );
-      SEARCH_PAGE_INPUT.dispatchEvent(new Event("input"))
-    };
-    SEARCH_INPUT.dispatchEvent(new Event("input"))
-  })
-  .catch(e => {
-    SEARCH_INPUT.addEventListener("input", ev => handleSearch(null, e, ev, ac_results, AC_MAX_RESULTS,true ));
-    if(SEARCH_PAGE_INPUT) {
-      SEARCH_PAGE_INPUT.addEventListener("input", ev => handleSearch(null, e, ev, SEARCH_RESULTS, SEARCH_PAGE_MAX_RESULTS, false));
-    }
-  });

static/site-root.js

@@ -1,4 +0,0 @@
-/**
- * Get the site root, {siteRoot} is to be replaced by doc-gen4.
- */
-export const SITE_ROOT = "{siteRoot}";