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Proof step 11 from proof update-putfis-sw (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 10:
∀ r, sk, val, st. update(r, fis0[sk, val], st) = (update(r, fis0, st)[r -- sk, val]) ⊦ sk = sk0, (update(r, fis0[sk, val], st)[r -- sk0, val0]) = (update(r, fis0, st)[r -- sk0, val0][r -- sk, val])

Rule argument

[emptyarg]

Additional information

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