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Proof step 9 from proof range-le (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
2 + m < nused, 2 + m < # zbrar, nused ≤ # zbrar ⊦ ((ri |≤ key) |> zbrar[m].key) |≤ zbrar[m + 1].key = (ri |> zbrar[m].key) |≤ zbrar[m + 1].key, key < zbrar[m + 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)