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Proof step 5 from proof update-put-same (previous step)

¬ ¬ sk ∈ fis0, sk ∈ (sk0 × val0) ' + fis0, ∀ sk, r, st, val. sk ∈ fis0 → update(r, fis0, st[r -- sk, val]) = update(r, fis0, st) ⊦ (update(r, fis0, st[r -- sk, val])[r -- sk0, val0]) = (update(r, fis0, st)[r -- sk0, val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
sk ∈ fis0, ∀ sk, r, st, val. sk ∈ fis0 → update(r, fis0, st[r -- sk, val]) = update(r, fis0, st) ⊦ (update(r, fis0, st[r -- sk, val])[r -- sk0, val0]) = (update(r, fis0, st)[r -- sk0, val0])

Rule argument

[emptyarg]

Additional information

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