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Proof step 14 from proof add-gins (previous step)

∀ r, class1, st, sk, val. (addobj(r, class1, fis0, st)[r -- sk, val]) = addobj(r, class1, fis0[sk, val], st) ⊦ (addobj(r, class1, fis0, st)[r -- fv .1, fv .2][r -- sk, val]) = addobj(r, class1, (fv ' + fis0)[sk, val], st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
fv = sk0 × val0, ∀ r, class1, st, sk, val. (addobj(r, class1, fis0, st)[r -- sk, val]) = addobj(r, class1, fis0[sk, val], st) ⊦ (addobj(r, class1, fis0, st)[r -- sk0, val0][r -- sk, val]) = addobj(r, class1, (fv ' + fis0)[sk, val], st)

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)]]