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Proof step 11 from proof dels-ignore-data (previous step)

key.data?, inodekey(ino) ∈ ro, key ∈ ri ⊦ # ro = 0, ((ri -- datakey(ino, n)) ⊖ ro)[key] = (ri ⊖ ro)[key], key = datakey(ino, n), ro = ∅, key ∈ ro, inodekey(key.ino) ∈ ro

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
key = datakey(m, m0), key.data?, key ∈ ri, inodekey(ino) ∈ ro ⊦ # ro = 0, ((ri -- datakey(ino, n)) ⊖ ro)[key] = (ri ⊖ ro)[key], key = datakey(ino, n), ro = ∅, inodekey(m) ∈ ro, key ∈ 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