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Proof step 30 from proof ac-shift (previous step)

is_fskey(fv .1), ∀ 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]) ⊦ fv .1 .fs .class = class1, class2 = class1, (addclass(class1, fis0, st)[jvmref -- mkfs(class2, ty, fieldvar) ', val]) = addclass(class1, fis0, st[jvmref -- mkfs(class2, ty, fieldvar) ', val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
fv = sk × val0, 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]) ⊦ sk .fs .class = class1, class2 = class1, (addclass(class1, fis0, st)[jvmref -- mkfs(class2, ty, fieldvar) ', val]) = addclass(class1, fis0, st[jvmref -- mkfs(class2, ty, fieldvar) ', val])

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk, val0] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk, val0)]]