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Proof step 4 from proof update-at (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 3:
∀ r, r0, st, sk. r = r0 ∨ (update(r0, fis0, st)[r -- sk]) = st[r -- sk] ⊦ r = r0, (update(r0, fis0, st)[r -- sk]) = st[r -- sk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]