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Proof step 30 from proof addclass-switch-01 (previous step)

is_fskey(fv .1), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ fv .1 .fs .class = class, r = jvmref, addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
fv = sk0 × val0, is_fskey(sk0), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ sk0 .fs .class = class, r = jvmref, addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val])

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk0, val0] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk0, val0)]]