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Proof step 8 from proof update-put-notin (previous step)

fv = sk0 × val0, ∀ r0, st, sk, val. (update(r0, fis0, st)[r0 -- sk, val]) = update(r0, fis0, st[r0 -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r0, fis0, st)[r0 -- sk0, val0][r0 -- sk, val]) = (update(r0, fis0, st[r0 -- sk, val])[r0 -- sk0, val0]), sk ∈ fv ', sk ∈ fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

[emptyarg]

Additional information

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