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Proof step 13 from proof replay-cons-add-orphan (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ (key ∈ ri ⊖ (ro ++ inodekey(ino)) ↔ key ∈ (ri ⊖ inodekey(ino)) ⊖ ro) ∧ (key ∈ ri ⊖ (ro ++ inodekey(ino)) → (ri ⊖ (ro ++ inodekey(ino)))[key] = ((ri ⊖ inodekey(ino)) ⊖ ro)[key])

Proof step 13 from proof replay-cons-add-orphan (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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