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Proof step 33 from proof replay-cons-add-orphan (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]

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 ++ inodekey(ino), ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ ks ++ key0 ↔ key ∈ ks); (s) Used terms: key, ro ++ inodekey(ino), ri