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Proof step 22 from proof del-commute-dels (previous step)

⊦ key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key, key ∈ ks

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0)
Proof step 24:
⊦ key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ ri ⊖ ks ∧ key0 ≠ key ∧ (key0.data? → inodekey(key0.ino) ≠ key), key ∈ ks

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 ⊖ ks, key0] flags: <all paths>

Additional information

Used terms: key, ri ⊖ ks, key0