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Proof step 8 from proof range-le (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
n = m + 1, n + 1 < # zbrar, n + 1 < nused, nused ≤ # zbrar ⊦ n = 0, ((ri |≤ key) |> zbrar[m].key) |≤ zbrar[n].key = (ri |> zbrar[m].key) |≤ zbrar[n].key, key < zbrar[n].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