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Proof step 7 from proof update-put-same (previous step)

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) .1, (sk0 × val0) .2]) = (update(r, fis0, st)[r -- (sk0 × val0) .1, (sk0 × val0) .2])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sk × val) .2 = val], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]