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Proof step 7 from proof range-le (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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

Rule argument

Additional information

Used simplifier rules: range-inner: ⊦ n ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri) = (ri |> zbrar[n - 1].key) |≤ zbrar[n].key;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic