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Proof step 28 from proof del-merge-dels (previous step)

key ∈ ks ⊦ # ks = 0, key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ ri ⊖ ks, ks = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks)
Proof step 30:
key ∈ ks ⊦ # ks = 0, key0 ∈ ri ⊖ key ∧ ¬ key0 ∈ ks ∧ (key0.data? → ¬ inodekey(key0.ino) ∈ ks) ↔ key0 ∈ ri ⊖ ks, ks = ∅

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 terms: ks, ri ⊖ key, key0