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Proof step 22 from proof keep-range (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
zbr.key = zbrar[m].key, n = m0 + 1, n + 1 < # zbrar, n < nused, m < # zbrar, n < # zbrar, n + 1 < nused, nused ≤ # zbrar ⊦ n = 0, (ri |> zbrar[m, zbr][m0].key) |≤ zbrar[m, zbr][n].key = (ri |> zbrar[m0].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, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m0