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Proof step 27 from proof replay-cons-add-page (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ks, ri] → [key, ro, ri -- datakey(ino, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s) Used terms: key, ro, ri -- datakey(ino, n)