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

key ∈ ks, key0 ∈ ri, key0.data? → ¬ inodekey(key0.ino) ∈ ks, key0.data? → inodekey(key0.ino) ≠ key ⊦ # ks = 0, ((ri ⊖ key) ⊖ ks)[key0] = (ri ⊖ ks)[key0], ks = ∅, key0 ∈ ks, key0 ∈ ri ⊖ key ∧ ¬ key0.data?

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used terms: key, ri, key0