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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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4
lean/Spa/Analysis/Forward/Adapters.lean
View File

@@ -10,7 +10,7 @@ def updateVariablesFromExpression (k : String) (e : Expr)
(vs : VariableValues L prog) : VariableValues L prog :=
FiniteMap.generalizedUpdate id (fun _ vs => E.eval e vs) [k] vs
theorem updateVariablesFromExpression_mono (k : String) (e : Expr) :
lemma updateVariablesFromExpression_mono (k : String) (e : Expr) :
Monotone (updateVariablesFromExpression (L := L) (prog := prog) k e) :=
FiniteMap.generalizedUpdate_monotone monotone_id (fun _ => E.eval_mono e)
@@ -20,7 +20,7 @@ def evalBasicStmt (_ : prog.State) (bs : BasicStmt)
| .assign k e => updateVariablesFromExpression k e vs
| .noop => vs
theorem evalBasicStmt_mono (s : prog.State) (bs : BasicStmt) :
lemma evalBasicStmt_mono (s : prog.State) (bs : BasicStmt) :
Monotone (evalBasicStmt (L := L) (prog := prog) s bs) := by
cases bs with
| assign k e => exact updateVariablesFromExpression_mono k e

20
lean/Spa/Analysis/Forward/Lattices.lean
View File

@@ -18,7 +18,7 @@ def botV [FiniteHeightLattice L] : VariableValues L prog :=
variable {L prog}
omit [Lattice L] in
theorem states_memKey (s : prog.State) (sv : StateVariables L prog) :
lemma states_memKey (s : prog.State) (sv : StateVariables L prog) :
FiniteMap.MemKey s sv :=
FiniteMap.MemKey_iff.mpr (prog.states_complete s)
@@ -27,11 +27,11 @@ def variablesAt (s : prog.State) (sv : StateVariables L prog) :
(FiniteMap.locate (states_memKey s sv)).1
omit [Lattice L] in
theorem variablesAt_mem (s : prog.State) (sv : StateVariables L prog) :
lemma variablesAt_mem (s : prog.State) (sv : StateVariables L prog) :
(s, variablesAt s sv) ∈ sv :=
(FiniteMap.locate (states_memKey s sv)).2
theorem variablesAt_le {sv₁ sv₂ : StateVariables L prog} (hle : sv₁ ≤ sv₂)
lemma variablesAt_le {sv₁ sv₂ : StateVariables L prog} (hle : sv₁ ≤ sv₂)
(s : prog.State) : variablesAt s sv₁ ≤ variablesAt s sv₂ :=
FiniteMap.le_of_mem_mem prog.states_nodup hle
(variablesAt_mem s sv₁) (variablesAt_mem s sv₂)
@@ -42,7 +42,7 @@ def joinForKey (k : prog.State) (sv : StateVariables L prog) :
VariableValues L prog :=
(sv.valuesAt (prog.incoming k)).foldr (· ⊔ ·) (botV L prog)
theorem joinForKey_mono (k : prog.State) :
lemma joinForKey_mono (k : prog.State) :
Monotone (joinForKey (L := L) k) := by
intro sv₁ sv₂ hle
exact foldr_mono _ (FiniteMap.valuesAt_le hle (prog.incoming k)) (le_refl _)
@@ -52,15 +52,15 @@ theorem joinForKey_mono (k : prog.State) :
def joinAll (sv : StateVariables L prog) : StateVariables L prog :=
FiniteMap.generalizedUpdate id joinForKey prog.states sv
theorem joinAll_mono : Monotone (joinAll (L := L) (prog := prog)) :=
lemma joinAll_mono : Monotone (joinAll (L := L) (prog := prog)) :=
FiniteMap.generalizedUpdate_monotone monotone_id joinForKey_mono
theorem joinAll_mem_eq {s : prog.State} {vs : VariableValues L prog}
lemma joinAll_mem_eq {s : prog.State} {vs : VariableValues L prog}
{sv : StateVariables L prog} (h : (s, vs) ∈ joinAll sv) :
vs = joinForKey s sv :=
FiniteMap.generalizedUpdate_mem_eq (prog.states_complete s) h
theorem variablesAt_joinAll (s : prog.State) (sv : StateVariables L prog) :
lemma variablesAt_joinAll (s : prog.State) (sv : StateVariables L prog) :
variablesAt s (joinAll sv) = joinForKey s sv :=
joinAll_mem_eq (variablesAt_mem s (joinAll sv))
@@ -74,12 +74,12 @@ instance : Interp (VariableValues L prog) (Env → Prop) where
∀ (k : String) (l : L), (k, l) ∈ vs →
∀ (v : Value), Env.Mem (k, v) ρ → I.interp l v
theorem interp_botV_nil : ⟦ botV L prog ⟧ [] := by
lemma interp_botV_nil : ⟦ botV L prog ⟧ [] := by
intro k l _ v hmem
cases hmem
omit [FiniteHeightLattice L] in
theorem interp_sup {vs₁ vs₂ : VariableValues L prog} {ρ : Env}
lemma interp_sup {vs₁ vs₂ : VariableValues L prog} {ρ : Env}
(h : ⟦ vs₁⟧ ρ ∨ ⟦ vs₂ ⟧ ρ) : ⟦ vs₁ ⊔ vs₂ ⟧ ρ := by
intro k l hmem v hv
obtain ⟨l₁, l₂, rfl, h₁, h₂⟩ := FiniteMap.mem_sup hmem
@@ -87,7 +87,7 @@ theorem interp_sup {vs₁ vs₂ : VariableValues L prog} {ρ : Env}
· exact I.interp_sup v (Or.inl (h _ _ h₁ _ hv))
· exact I.interp_sup v (Or.inr (h _ _ h₂ _ hv))
theorem interp_foldr {vs : VariableValues L prog}
lemma interp_foldr {vs : VariableValues L prog}
{vss : List (VariableValues L prog)} {ρ : Env}
(hvs : ⟦ vs ⟧ ρ) (hmem : vs ∈ vss) :
⟦ vss.foldr (· ⊔ ·) (botV L prog) ⟧ ρ := by