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Proof step 36 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 ⊖ inodekey(ino)) ⊖ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks)
Proof step 38:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ key ∈ ri ⊖ (ro ++ inodekey(ino)) ↔ key ∈ ri ⊖ inodekey(ino) ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro)

Rule argument

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

Additional information

Used terms: ro, ri ⊖ inodekey(ino), key