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Proof step 12 from proof look-subrange (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: n + 1 = nused

Additional information

Used simplifier rules: ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0; (s)% ⊦ key0 ∈ ri |> key1 ↔ key0 ∈ ri ∧ key1 < key0; (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 ≤ n ↔ m < n; (s) Used formulas: n + 1 = nused