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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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12
lean/Spa/Analysis/Constant.lean
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@@ -27,13 +27,13 @@ def minus : ConstLattice → ConstLattice → ConstLattice
| _, top => top
| mk z₁, mk z₂ => mk (z₁ - z₂)
theorem plus_mono₂ : Monotone₂ plus :=
lemma plus_mono₂ : Monotone₂ plus :=
AboveBelow.monotone₂_of_strict plus
(fun y => by cases y <;> rfl) (fun x => by cases x <;> rfl)
(fun y hy => by cases y <;> first | exact absurd rfl hy | rfl)
(fun x hx => by cases x <;> first | exact absurd rfl hx | rfl)
theorem minus_mono₂ : Monotone₂ minus :=
lemma minus_mono₂ : Monotone₂ minus :=
AboveBelow.monotone₂_of_strict minus
(fun y => by cases y <;> rfl) (fun x => by cases x <;> rfl)
(fun y hy => by cases y <;> first | exact absurd rfl hy | rfl)
@@ -44,7 +44,7 @@ def interpConst : ConstLattice → Value → Prop
| .top, _ => True
| .mk z, v => v = .int z
theorem interpConst_mk_disjoint {z₁ z₂ : ℤ} (hne : z₁ ≠ z₂) {v : Value} :
lemma interpConst_mk_disjoint {z₁ z₂ : ℤ} (hne : z₁ ≠ z₂) {v : Value} :
¬(interpConst (.mk z₁) v ∧ interpConst (.mk z₂) v) := by
rintro ⟨h₁, h₂⟩
rw [h₁] at h₂
@@ -65,7 +65,7 @@ def eval : Expr → VariableValues ConstLattice prog → ConstLattice
if h : FiniteMap.MemKey k vs then (FiniteMap.locate h).1 else .top
| .num n, _ => .mk n
theorem eval_mono (e : Expr) : Monotone (eval prog e) := by
lemma eval_mono (e : Expr) : Monotone (eval prog e) := by
induction e with
| add e₁ e₂ ih₁ ih₂ =>
intro vs₁ vs₂ h
@@ -93,7 +93,7 @@ instance exprEvaluator : ExprEvaluator ConstLattice prog :=
def output : String :=
show' (result ConstLattice prog)
theorem plus_valid {g₁ g₂ : ConstLattice} {z₁ z₂ : ℤ}
lemma plus_valid {g₁ g₂ : ConstLattice} {z₁ z₂ : ℤ}
(h₁ : ⟦g₁⟧ (.int z₁)) (h₂ : ⟦g₂⟧ (.int z₂)) :
⟦plus g₁ g₂⟧ (.int (z₁ + z₂)) := by
rcases g₁ with _ | _ | c₁
@@ -110,7 +110,7 @@ theorem plus_valid {g₁ g₂ : ConstLattice} {z₁ z₂ : ℤ}
show Value.int (z₁ + z₂) = Value.int (c₁ + c₂)
rw [hz₁, hz₂]
theorem minus_valid {g₁ g₂ : ConstLattice} {z₁ z₂ : ℤ}
lemma minus_valid {g₁ g₂ : ConstLattice} {z₁ z₂ : ℤ}
(h₁ : ⟦g₁⟧ (.int z₁)) (h₂ : ⟦g₂⟧ (.int z₂)) :
⟦minus g₁ g₂⟧ (.int (z₁ - z₂)) := by
rcases g₁ with _ | _ | c₁