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Proof step 9 from proof update-put-same (previous step)

∀ sk, r, st, val. sk ∈ fis0 → update(r, fis0, st[r -- sk, val]) = update(r, fis0, st), sk ∈ fv + fis0 ⊦ update(r, fv + fis0, st[r -- sk, val]) = update(r, fv + fis0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ update(r, fv ' + fis, st) = (update(r, fis, st)[r -- fv .1, fv .2])
Proof step 8:
sk ∈ fv ' + 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 -- fv .1, fv .2]) = (update(r, fis0, st)[r -- fv .1, fv .2])

Rule argument

[emptyarg]

Additional information

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