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Proof step 11 from proof del-del-again (previous step)

key.data?, inodekey(m) ∈ ks, key ∈ ri ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[key] = (ri ⊖ ks)[key], ks = ∅, key ∈ ks, inodekey(key.ino) ∈ ks

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
key = datakey(m0, m1), key.data?, key ∈ ri, inodekey(m) ∈ ks ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[key] = (ri ⊖ ks)[key], ks = ∅, inodekey(m0) ∈ ks, key ∈ ks

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, m0, m1]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m0, m1