Theorems · Theorem · real analysis

Finset.sum_eq_sum_range_intervalGapsWithin

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : AddCommGroup β] (F : Finset (α × α)) {k : ℕ}
  (h : F.card = k) {a b : α} (f : α → α → β),
  ∑ z ∈ F, f z.1 z.2 = ∑ i ∈ Finset.range k, f (F.intervalGapsWithin h a b ↑i).2 (F.intervalGapsWithin h a b ↑i.succ).1

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Gaps

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderAddCommGroup