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Proof step 10 from proof add-nput (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ sk, r, class1, st, val. sk = _type ∨ (addobj(r, class1, fis0, st)[r -- sk, val]) = addobj(r, class1, fis0, st[r -- sk, val]) ∨ sk ∈ fis0 ⊦ sk = _type, (addobj(r, class1, fis0, st)[r -- sk0, val0][r -- sk, val]) = (addobj(r, class1, fis0, st[r -- sk, val])[r -- sk0, val0]), sk = sk0, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

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