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Proof step 12 from proof add-nput (previous step)

∀ 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, fv + fis0, st)[r -- sk, val]) = addobj(r, class1, fv + fis0, st[r -- sk, val]), sk ∈ fv + fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ addobj(r, class1, fv ' + fis, st) = (addobj(r, class1, fis, st)[r -- fv .1, fv .2])
Proof step 11:
∀ 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 -- fv .1, fv .2][r -- sk, val]) = (addobj(r, class1, fis0, st[r -- sk, val])[r -- fv .1, fv .2]), sk ∈ fv ', sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ fis + fis0 ↔ sk ∈ fis ∨ sk ∈ fis0], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]