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Proof step 9 from proof ac-mode-01 (previous step)

sk .fs = mkfs(class, ty, fieldvar), is_fskey(sk), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, (addclass(class, (sk × val) ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
sk = fs ', fs = mkfs(class, ty, fieldvar), is_fskey(sk), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, (addclass(class, (sk × val) ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

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)]]