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Proof step 20 from proof ac-init-01 (previous step)

initundone(class1, addclass(class1, (sk × val) ' + fis0, st)), is_fskey(sk), ∀ class1, st. initundone(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class1, void_type, `initstate' .field) ' = sk, mkfs(class1, void_type, `initstate' .field) ' ∈ fis0, ¬ is_indexkey(sk) ∧ sk .fs .class ≠ class1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
sk = fs ', initundone(class1, addclass(class1, (sk × val) ' + fis0, st)), is_fskey(sk), ∀ class1, st. initundone(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class1, void_type, `initstate' .field) ' = sk, mkfs(class1, void_type, `initstate' .field) ' ∈ fis0, ¬ is_indexkey(sk) ∧ fs .class ≠ class1

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]