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Proof step 27 from proof del-commute-dels (previous step)

⊦ key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ ri ∧ ¬ key0 ∈ ks ∧ (key0.data? → ¬ inodekey(key0.ino) ∈ ks) ∧ key0 ≠ key ∧ (key0.data? → inodekey(key0.ino) ≠ key), key ∈ ks

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: in-dels-ro seq: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks) subst: [ks, ri, key] → [ks, ri ⊖ key, key0] flags: <all paths>

Additional information

Used simplifier rules: in-del-ro: ⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0); Used terms: ks, ri ⊖ key, key0