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Proof step 9 from proof update-putfis-sw (previous step)

r -- sk ≠ r -- sk0, ∀ 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 -- sk, val][r -- sk0, val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ 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 -- sk, val][r -- sk0, val0])

Rule argument

[emptyarg]

Additional information

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