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Proof step 9 from proof replay-cons-add-orphan (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ replay-log(log, fs, fi ⊖ fo) = ri ⊖ (ro ++ inodekey(ino)) ↔ replay-log(log, fs, fi ⊖ fo) = (ri ⊖ inodekey(ino)) ⊖ ro

User applied rule cut formula

And obtained the following new goals

Proof step 10:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ replay-log(log, fs, fi ⊖ fo) = ri ⊖ (ro ++ inodekey(ino)) ↔ replay-log(log, fs, fi ⊖ fo) = (ri ⊖ inodekey(ino)) ⊖ ro, ri ⊖ (ro ++ inodekey(ino)) = (ri ⊖ inodekey(ino)) ⊖ ro

Rule argument

fma: ri ⊖ (ro ++ inodekey(ino)) = (ri ⊖ inodekey(ino)) ⊖ ro

Additional information

Used formulas: ri ⊖ (ro ++ inodekey(ino)) = (ri ⊖ inodekey(ino)) ⊖ ro