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Proof step 7 from proof ac-in-08 (previous step)

sk .fs = mkfs(class, ty, fieldvar), r ∈ st, is_fskey(sk), ∀ r, st, class1. r ∈ st → r ∈ addclass(class1, fis0, st) ⊦ r ∈ addclass(class1, (sk × val) ' + fis0, st), class ≠ class1 ∧ ¬ is_indexkey(sk)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 6:
⊦ r ≠ jvmref → (r ∈ addclass(class1, fis, st) ↔ r ∈ st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ ¬ is_indexkey(fs ')], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ r ∈ st[r0 -- sk, val] ↔ r = r0 ∨ r ∈ st], [CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]