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Proof step 2 from proof range-le (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n + 1 < nused, n + 1 < # zbrar, nused ≤ # zbrar ⊦ key-range(zbrar, n, nused, ri |≤ key) = key-range(zbrar, n, nused, ri), key < zbrar[n].key

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ key0 ≤ key1 ↔ ¬ key1 < key0; (s)