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Proof step 13 from proof addclass-switch-01 (previous step)

sk0 .fs = mkfs(class, ty, fieldvar), is_fskey(sk0), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ addclass(class, (sk0 × val0) ' + fis0, st[r -- sk, val]) = (addclass(class, (sk0 × val0) ' + fis0, st)[r -- sk, val]), r = jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
sk0 = fs ', fs = mkfs(class, ty, fieldvar), is_fskey(sk0), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ addclass(class, (sk0 × val0) ' + fis0, st[r -- sk, val]) = (addclass(class, (sk0 × val0) ' + fis0, st)[r -- sk, val]), r = jvmref

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk0, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk0, fs)]]