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Proof step 8 from proof look-subrange (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 9:
n < nused, n < # zbrar, key ∈ (n = 0 ⊃ (nused = 1 ⊃ ri;ri |≤ zbrar[0].key);(n + 1 = nused ⊃ ri |> zbrar[n - 1].key;(ri |> zbrar[n - 1].key) |≤ zbrar[n].key)), nused ≤ # zbrar ⊦ nused = 1, key ∈ ri

Rule argument

fma: nused = 1

Additional information

Used simplifier rules: ⊦ 1 = m + 1 ↔ m = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < 1 ↔ m = 0; (s) Used formulas: nused = 1