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Proof step 7 from proof add-notin (previous step)

∀ sk, r, class, st. sk = _type ∨ (addobj(r, class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = fv .1, sk = _type, (addobj(r, class, fis0, st)[r -- sk]) = st[r -- sk], sk ∈ fis0, sk ∈ fv '

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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

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)]]