Theorems · Theorem · group theory

Finset.sum_Ico_add

∀ {α : Type u_1} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid α] [inst_2 : PartialOrder α]
  [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α] [inst_5 : LocallyFiniteOrder α] (f : α → M) (a b c : α),
  ∑ x ∈ Finset.Ico a b, f (c + x) = ∑ x ∈ Finset.Ico (a + c) (b + c), f x

Defined in

Mathlib.Algebra.BigOperators.Intervals

Cited by

5 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoidPartialOrderIsOrderedCancelAddMonoidExistsAddOfLELocallyFiniteOrder