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Proof step 18 from proof ac-shift-03 (previous step)

is_fskey(sk), ∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st) ⊦ (addclass(sk .fs .class, (sk × val0) ' + fis0, st)[jvmref -- mkfs(sk .fs .class, ty, fieldvar) ', val]) = addclass(sk .fs .class, ((sk × val0) ' + fis0)[mkfs(sk .fs .class, ty, fieldvar) ', val], st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
sk = fs ', is_fskey(sk), ∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st) ⊦ (addclass(fs .class, (sk × val0) ' + fis0, st)[jvmref -- mkfs(fs .class, ty, fieldvar) ', val]) = addclass(fs .class, ((sk × val0) ' + fis0)[mkfs(fs .class, ty, fieldvar) ', val], st)

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)]]