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Proof step 5 from proof update-put (previous step)

r -- sk ≠ r0 -- sk0, ∀ 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)[r -- sk, val][r0 -- sk0, val0]) = (update(r0, fis0, st[r -- sk, val])[r0 -- sk0, val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ 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)[r -- sk, val][r0 -- sk0, val0]) = (update(r0, fis0, st[r -- sk, val])[r0 -- sk0, val0])

Rule argument

[emptyarg]

Additional information

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