GolangLean/Core/Preservation.lean:
theorem preservation:
HasType Γ e T -> HasTypeH ht h -> HasTypeEnv ht env Γ ->
BigStep h env e v h' ->
∃ ht', HeapTy.extends ht ht' /\ HasTypeH ht' h' /\
HasTypeV ht' v T /\ HasTypeEnv ht' env Γ
The standard big-step type-soundness result: well-typed terminating
programs produce well-typed values, with heap conformance preserved.
Proof is by induction on the big-step derivation, fourteen cases.
Supporting infrastructure:
HeapTy.extends_push - heap-typing extends across a push
HasTypeH.push - heap conformance preserved by push
HasTypeH.setIfInBounds - heap conformance preserved by in-bounds update
binop_apply_sound - operator typing matches operator semantics
The closure case (appR) uses the mutual HasTypeV/HasTypeEnv weakening
lemmas from TypeSoundness to thread heap-typings across the three
sub-derivations. The assign case (assignR) uses the heap-update
lemma to preserve conformance. The if-cases collapse the cross-rule
(ifT vs ifF) ambiguity via Bool.noConfusion on the condition's IH.
Zero sorries / axioms / admits across the project. Full lake build clean.
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