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Proof step 19 from proof replay-orphans-dentry (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
key = datakey(m, m0), key.data?, key ∈ ri ⊦ (ri ⊖ ro)[key] = (ri[dentrykey(ino, str), adr] ⊖ ro)[key], key = dentrykey(ino, str), inodekey(m) ∈ ro, key ∈ ro, dentrykey(ino, str) ∈ ro

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key, m, m0]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m, m0