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Proof step 28 from proof replay-orphans-dentry (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ks, ri] → [key, ro, ri[dentrykey(ino, str), adr]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s) Used terms: key, ro, ri[dentrykey(ino, str), adr]