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Proof step 8 from proof add-nput-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ 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 = sk0, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' ↔ sk = sk0])]]