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

∀ r, r0, st, sk, val. r = r0 ∨ (update(r0, fis0, st)[r -- sk, val]) = update(r0, fis0, st[r -- sk, val]) ⊦ r = r0, (update(r0, fv + fis0, st)[r -- sk, val]) = update(r0, fv + fis0, st[r -- sk, val])

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, r0, st, sk, val. r = r0 ∨ (update(r0, fis0, st)[r -- sk, val]) = update(r0, fis0, st[r -- sk, val]) ⊦ r = r0, (update(r0, fis0, st)[r0 -- fv .1, fv .2][r -- sk, val]) = (update(r0, fis0, st[r -- sk, val])[r0 -- fv .1, fv .2])

Rule argument

[emptyarg]

Additional information

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