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Proof step 9 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, fv + fis0, st[r -- sk, val]) = (update(r, fv + fis0, st)[r -- sk, val]), sk ∈ fv + fis0

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:
∀ 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 -- fv .1, fv .2]) = (update(r, fis0, st)[r -- fv .1, fv .2][r -- sk, val]), sk ∈ fv ', sk ∈ fis0

Rule argument

[emptyarg]

Additional information

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