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Proof step 40 from proof replay-cons-add-orphan (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ key ∈ ri ⊖ (ro ++ inodekey(ino)) ↔ (key ∈ ri ∧ key ≠ inodekey(ino) ∧ (key.data? → inodekey(key.ino) ≠ inodekey(ino))) ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ key ∈ ri ⊖ (ro ++ inodekey(ino)) ↔ key ∈ ri ∧ key ≠ inodekey(ino) ∧ (key.data? → key.ino ≠ ino) ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro)

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)