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Proof step 26 from proof replay-cons-add-page (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo), key ∈ ri, key.data? → ¬ inodekey(key.ino) ∈ ro ⊦ ri[key] = ((ri -- datakey(ino, n)) ⊖ ro)[key], key = datakey(ino, n), key.data?, key ∈ ro, key ∈ ro ++ datakey(ino, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo), key ∈ ri ⊦ ri[key] = ((ri -- datakey(ino, n)) ⊖ ro)[key], key = datakey(ino, n), key.data?, key ∈ ro

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ ks ++ key0 ↔ key ∈ ks); (s)