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Proof step 13 from proof at-range (previous step)

n + 1 < nused, n < nused, n < # zbrar, zbrar[n - 1].key < key, n + 1 < # zbrar, key ∈ ri, nused ≤ # zbrar ⊦ ((ri |> zbrar[n - 1].key) |≤ zbrar[n].key)[key] = ri[key], n = 0, zbrar[n].key < key

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
n = m + 1, n + 1 < # zbrar, zbrar[m].key < key, n < # zbrar, n < nused, n + 1 < nused, key ∈ ri, nused ≤ # zbrar ⊦ ((ri |> zbrar[m].key) |≤ zbrar[n].key)[key] = ri[key], n = 0, zbrar[n].key < key

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m