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Proof step 6 from proof range-le (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: nused

Additional information

Used simplifier rules: range-first: ⊦ nused ≠ 0 ∧ nused < # zbrar → key-range(zbrar, 0, nused + 1, ri) = ri |≤ zbrar[0].key;%nat freely generated by 0, +1;;% ⊦ m +1 = m + 1; (s)% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ key0 < key1 → ri |≤ key0 |≤ key1 = ri |≤ key1; (s)