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Proof step 21 from proof del-put-again (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: node-index name: In-insert seq: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri subst: [adr, key0, ri, key] → [adr, inodekey(m), ri, key] flags: <all paths>

Additional information

Used simplifier rules: in-dels-ro: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); Used terms: adr, inodekey(m), ri, key