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Proof step 31 from proof replay-orphans-dentry (previous step)

⊦ key ∈ ri ⊖ ro ↔ key ∈ ri[dentrykey(ino, str), adr] ⊖ ro, key = dentrykey(ino, str), dentrykey(ino, str) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

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[dentrykey(ino, str), adr], key] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws) Used terms: ro, ri[dentrykey(ino, str), adr], key