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Proof step 9 from proof ac-lookup-04 (previous step)

is_fskey(sk0), ∀ r, class1, st, sk. r = jvmref ∨ (addclass(class1, fis0, st)[r -- sk]) = st[r -- sk] ⊦ r = jvmref, (addclass(class1, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk], ¬ is_indexkey(sk0) ∧ sk0 .fs .class ≠ class1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
sk0 = fs ', is_fskey(sk0), ∀ r, class1, st, sk. r = jvmref ∨ (addclass(class1, fis0, st)[r -- sk]) = st[r -- sk] ⊦ r = jvmref, (addclass(class1, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk], ¬ is_indexkey(sk0) ∧ fs .class ≠ class1

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)]]