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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ r, st, sk, val. update(r, fis0, st[r -- sk, val]) = (update(r, fis0, st)[r -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r, fis0, st[r -- sk, val])[r -- sk0, val0]) = (update(r, fis0, st)[r -- sk0, val0][r -- sk, val]), sk = sk0, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' ↔ sk = sk0], [CSIMPSEQ : ⊦ (sk × val) .2 = val], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]