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Adopt lemma as the default keyword

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Convert every theorem to lemma (mathlib's default) except the headline results a
reader of each module seeks out: analyze_correct (Forward/Sign/Constant),
aFix_eq/aFix_le (Fixedpoint), trace (Language), and Stmt.cfg_sufficient
(Language/Properties). lemma and theorem are interchangeable keywords, so no
references change.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-25 13:59:08 -05:00
parent 5c9c8ac55c
commit e2df847139
20 changed files with 143 additions and 143 deletions
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10
lean/Spa/Lattice.lean
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@@ -11,7 +11,7 @@ section Folds
variable {α β : Type*} [Preorder α] [Preorder β]
theorem foldr_mono {l₁ l₂ : List α} (f : α → β → β) {b₁ b₂ : β}
lemma foldr_mono {l₁ l₂ : List α} (f : α → β → β) {b₁ b₂ : β}
(hl : List.Forall₂ (· ≤ ·) l₁ l₂) (hb : b₁ ≤ b₂)
(hf₁ : ∀ b, Monotone fun a => f a b) (hf₂ : ∀ a, Monotone (f a)) :
l₁.foldr f b₁ ≤ l₂.foldr f b₂ := by
@@ -20,7 +20,7 @@ theorem foldr_mono {l₁ l₂ : List α} (f : α → β → β) {b₁ b₂ : β}
| cons hxy _ ih =>
exact le_trans (hf₁ _ hxy) (hf₂ _ ih)
theorem foldl_mono {l₁ l₂ : List α} (f : β → α → β) {b₁ b₂ : β}
lemma foldl_mono {l₁ l₂ : List α} (f : β → α → β) {b₁ b₂ : β}
(hl : List.Forall₂ (· ≤ ·) l₁ l₂) (hb : b₁ ≤ b₂)
(hf₁ : ∀ a, Monotone fun b => f b a) (hf₂ : ∀ b, Monotone (f b)) :
l₁.foldl f b₁ ≤ l₂.foldl f b₂ := by
@@ -30,7 +30,7 @@ theorem foldl_mono {l₁ l₂ : List α} (f : β → α → β) {b₁ b₂ : β}
exact ih (le_trans (hf₁ _ hb) (hf₂ _ hxy))
omit [Preorder α] in
theorem foldr_mono' (l : List α) (f : α → β → β)
lemma foldr_mono' (l : List α) (f : α → β → β)
(hf : ∀ a, Monotone (f a ·)) : Monotone fun b => l.foldr f b := by
intro b₁ b₂ hb
induction l with
@@ -38,7 +38,7 @@ theorem foldr_mono' (l : List α) (f : α → β → β)
| cons x xs ih => exact hf x ih
omit [Preorder α] in
theorem foldl_mono' (l : List α) (f : β → α → β)
lemma foldl_mono' (l : List α) (f : β → α → β)
(hf : ∀ a, Monotone (f · a)) : Monotone fun b => l.foldl f b := by
intro b₁ b₂ hb
induction l generalizing b₁ b₂ with
@@ -65,7 +65,7 @@ namespace FiniteHeightLattice
variable (α : Type*) [Lattice α] [FiniteHeightLattice α]
theorem bot_le (a : α) : (⊥ : α) ≤ a := by
lemma bot_le (a : α) : (⊥ : α) ≤ a := by
by_cases heq : ⊥ ⊓ a = ⊥
· exact inf_eq_left.mp heq
· exfalso