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Proof step 10 from proof in-keyrange-in-ri-data (previous step)

adr ∈ ri |≤ zbrar[0].key, nused ≤ # zbrar ⊦ # zbrar = 0, nused = 1, nused = 0, adr ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri |≤ zbrar[0].key, adr] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0; (s)% ⊦ ¬ key1 < key0 ∧ key0 ∈ ri → (ri |≤ key1)[key0] = ri[key0]; (s)%key ∈ ri ⊦ ri[key] ∈ ri; (s) Used terms: ri |≤ zbrar[0].key, adr