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Proof step 22 from proof in-keyrange-in-ri-data (previous step)

2 + m < nused, m + 1 < nused, 2 + m < # zbrar, m + 1 < # zbrar, adr ∈ (ri |> zbrar[m].key) |≤ zbrar[m + 1].key, nused ≤ # zbrar ⊦ 2 + m = nused, adr ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 24:
m + 1 < # zbrar, 2 + m < # zbrar, m + 1 < nused, 2 + m < nused, nused ≤ # zbrar, ∃ key. key ∈ (ri |> zbrar[m].key) |≤ zbrar[m + 1].key ∧ ((ri |> zbrar[m].key) |≤ zbrar[m + 1].key)[key] = adr ⊦ 2 + m = nused, adr ∈ ri

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[m].key) |≤ zbrar[m + 1].key, adr] flags: <all paths>

Additional information

Used terms: (ri |> zbrar[m].key) |≤ zbrar[m + 1].key, adr