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Proof step 31 from proof addclass-switch (previous step)

is_indexkey(fv .1), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
fv = sk × val0, is_indexkey(sk), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val])

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)]]