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Proof step 9 from proof ac-lookup-06 (previous step)

is_fskey(sk0), ∀ sk, class, st, r. sk = mkfs(class, void_type, `initstate' .field) ' ∨ (addclass(class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = sk0, (addclass(sk0 .fs .class, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk], sk = mkfs(sk0 .fs .class, void_type, `initstate' .field) ', sk ∈ fis0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
sk0 = fs ', is_fskey(sk0), ∀ sk, class, st, r. sk = mkfs(class, void_type, `initstate' .field) ' ∨ (addclass(class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = sk0, (addclass(fs .class, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk], sk = mkfs(fs .class, void_type, `initstate' .field) ', sk ∈ fis0

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk0, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk0, fs)]]