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

∀ r, st, r0, sk. (update(r, fis0, st)[r0 -- sk]) = st[r0 -- sk] ∨ sk ∈ fis0 ⊦ (update(r, fis0, st)[r -- (sk0 × val) .1, (sk0 × val) .2][r0 -- sk]) = st[r0 -- sk], sk ∈ (sk0 × val) ', sk ∈ fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ r, st, r0, sk. (update(r, fis0, st)[r0 -- sk]) = st[r0 -- sk] ∨ sk ∈ fis0 ⊦ sk = sk0, (update(r, fis0, st)[r0 -- sk]) = st[r0 -- sk], sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' ↔ sk = sk0], [CSIMPSEQ : ⊦ (sk × val) .2 = val], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]