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Proof step 22 from proof replay-orphans-trunc (previous step)

key ∈ ro ⊦ # ro = 0, key0 ∈ (ri \ datakeys(key, n, ri)) ⊖ ro ↔ key0 ∈ ri ⊖ ro, ro = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks)
Proof step 24:
key ∈ ro ⊦ # ro = 0, key0 ∈ (ri \ datakeys(key, n, ri)) ⊖ ro ↔ key0 ∈ ri ∧ ¬ key0 ∈ ro ∧ (key0.data? → ¬ inodekey(key0.ino) ∈ ro), 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, key0] flags: <all paths>

Additional information

Used terms: ro, ri, key0