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Proof step 11 from proof del-commute-dels (previous step)

key0.data?, key0 ∈ ri ⊦ ((ri ⊖ key) ⊖ ks)[key0] = ((ri ⊖ ks) ⊖ key)[key0], inodekey(key0.ino) = key, key0 = key, key ∈ ks, key0 ∈ ks, inodekey(key0.ino) ∈ ks

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
key0 = datakey(m, m0), key0.data?, key0 ∈ ri ⊦ ((ri ⊖ key) ⊖ ks)[key0] = ((ri ⊖ ks) ⊖ key)[key0], inodekey(m) = key, key0 = key, inodekey(m) ∈ ks, key0 ∈ 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] → [key0, m, m0]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key0, m, m0