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