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Proof step 13 from proof ac-shift (previous step)

sk .fs = mkfs(class1, ty0, fieldvar0), is_fskey(sk), ∀ class2, class1, st, ty, fieldvar, val. class2 = class1 ∨ (addclass(class1, fis0, st)[jvmref -- mkfs(class2, ty, fieldvar) ', val]) = addclass(class1, fis0, st[jvmref -- mkfs(class2, ty, fieldvar) ', val]) ⊦ (addclass(class1, (sk × val0) ' + fis0, st)[jvmref -- mkfs(class2, ty, fieldvar) ', val]) = addclass(class1, (sk × val0) ' + fis0, st[jvmref -- mkfs(class2, ty, fieldvar) ', val]), class2 = class1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
sk = fs ', fs = mkfs(class1, ty0, fieldvar0), is_fskey(sk), ∀ class2, class1, st, ty, fieldvar, val. class2 = class1 ∨ (addclass(class1, fis0, st)[jvmref -- mkfs(class2, ty, fieldvar) ', val]) = addclass(class1, fis0, st[jvmref -- mkfs(class2, ty, fieldvar) ', val]) ⊦ (addclass(class1, (sk × val0) ' + fis0, st)[jvmref -- mkfs(class2, ty, fieldvar) ', val]) = addclass(class1, (sk × val0) ' + fis0, st[jvmref -- mkfs(class2, ty, fieldvar) ', val]), class2 = 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)]]