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Proof step 5 from proof add-nput-01 (previous step)

r -- sk ≠ r -- sk0, ∀ r, class1, sk, val, fis0, st. addobj(r, class1, fis1 + (sk × val) ' + fis0, st) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val]) ∨ sk ∈ fis1 ⊦ (addobj(r, class1, fis1 + (sk × val) ' + fis0, st)[r -- sk0, val0]) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val][r -- sk0, val0]), sk = sk0, sk ∈ fis1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ r, class1, sk, val, fis0, st. addobj(r, class1, fis1 + (sk × val) ' + fis0, st) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val]) ∨ sk ∈ fis1 ⊦ (addobj(r, class1, fis1 + (sk × val) ' + fis0, st)[r -- sk0, val0]) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val][r -- sk0, val0]), sk = sk0, sk ∈ fis1

Rule argument

[emptyarg]

Additional information

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