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Proof step 6 from proof update-put-notin (previous step)

r0 -- sk ≠ r0 -- sk0, ∀ r0, st, sk, val. (update(r0, fis0, st)[r0 -- sk, val]) = update(r0, fis0, st[r0 -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r0, fis0, st)[r0 -- sk, val][r0 -- sk0, val0]) = (update(r0, fis0, st[r0 -- sk, val])[r0 -- sk0, val0]), sk = sk0, sk ∈ fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ r0, st, sk, val. (update(r0, fis0, st)[r0 -- sk, val]) = update(r0, fis0, st[r0 -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r0, fis0, st)[r0 -- sk, val][r0 -- sk0, val0]) = (update(r0, fis0, st[r0 -- sk, val])[r0 -- sk0, val0]), sk = sk0, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]