Sum of integers below 133

Proved

FiniteTriangular.sum_range_133

by carlok · Sep 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticfinite-sum

The sum of the nonnegative integers strictly less than $133$ equals $8778$ . Equivalently, $\sum_{k=0}^{133-1} k = 133(133-1)/2$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular

theorem sum_range_133 : ∑ k ∈ range 133, k = 8778 := by sorry

end FiniteTriangular

Source

Elementary arithmetic series: the sum of the first m positive integers is m(m+1)/2, rewritten on Finset.range.