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Proof step 9 from proof add-nput-02 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
fv = sk0 × val0, ∀ r, class1, sk, val, st. addobj(r, class1, fis0 + (sk × val) ', st) = (addobj(r, class1, fis0, st)[r -- sk, val]) ∨ sk ∈ fis0 ⊦ (addobj(r, class1, fis0 + (sk × val) ', st)[r -- sk0, val0]) = (addobj(r, class1, fis0, st)[r -- sk0, val0][r -- sk, val]), sk ∈ fv ', sk ∈ fis0

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)]]