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Proof step 23 from proof keep-range (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
zbr.key = zbrar[m].key, 2 + m0 < nused, m < # zbrar, m0 + 1 < nused, 2 + m0 < # zbrar, m0 + 1 < # zbrar, nused ≤ # zbrar ⊦ (ri |> zbrar[m, zbr][m0].key) |≤ zbrar[m, zbr][m0 + 1].key = (ri |> zbrar[m0].key) |≤ zbrar[m0 + 1].key

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)