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Proof step 25 from proof in-keyrange-in-ri-data (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: node-index-restrict name: at-le seq: ⊦ ¬ key1 < key0 ∧ key0 ∈ ri → (ri |≤ key1)[key0] = ri[key0] subst: [key0, key1, ri] → [key, zbrar[m + 1].key, ri |> zbrar[m].key] 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: key, zbrar[m + 1].key, ri |> zbrar[m].key