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Proof step 30 from proof ac-shift-02 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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

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)]]