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Proof step 7 from proof add-in-09 (previous step)

sk ∈ fv ' + fis0, ∀ sk, r, class, st. sk ∈ fis0 → (addobj(r, class, fis0, st)[r -- sk]) = fis0[sk] ⊦ ((sk = fv .1 ⊃ fv .2; addobj(r, class, fis0, st)[r -- sk])) = (fv ' + fis0)[sk]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
fv = sk0 × val, sk ∈ fv ' + fis0, ∀ sk, r, class, st. sk ∈ fis0 → (addobj(r, class, fis0, st)[r -- sk]) = fis0[sk] ⊦ ((sk = sk0 ⊃ val; addobj(r, class, fis0, st)[r -- sk])) = (fv ' + fis0)[sk]

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk0, val] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk0, val)]]