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Proof step 8 from proof ao-put (previous step)

r0 -- sk ≠ r -- sk0, ∀ r, r0, class1, st, sk, val. r = r0 ∨ (addobj(r, class1, fis0, st)[r0 -- sk, val]) = addobj(r, class1, fis0, st[r0 -- sk, val]) ⊦ r = r0, (addobj(r, class1, fis0, st)[r0 -- sk, val][r -- sk0, val0]) = (addobj(r, class1, fis0, st[r0 -- sk, val])[r -- sk0, val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ r, r0, class1, st, sk, val. r = r0 ∨ (addobj(r, class1, fis0, st)[r0 -- sk, val]) = addobj(r, class1, fis0, st[r0 -- sk, val]) ⊦ r = r0, (addobj(r, class1, fis0, st)[r0 -- sk, val][r -- sk0, val0]) = (addobj(r, class1, fis0, st[r0 -- sk, val])[r -- sk0, val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]