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Proof step 15 from proof addclass-switch (previous step)

is_fskey(sk), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, (sk × val0) ' + fis0, st[r -- i ', val]) = (addclass(class, (sk × val0) ' + fis0, st)[r -- i ', val]), ¬ is_indexkey(sk) ∧ sk .fs .class ≠ class

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
sk = fs ', is_fskey(sk), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, (sk × val0) ' + fis0, st[r -- i ', val]) = (addclass(class, (sk × val0) ' + fis0, st)[r -- i ', val]), ¬ is_indexkey(sk) ∧ fs .class ≠ class

Rule argument

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

Additional information

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