Theorems · Theorem · group theory

finsum_mem_insert

∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] {a : α} {s : Set α} (f : α → M),
  a ∉ s → s.Finite → ∑ᶠ (i : α) (_ : i ∈ insert a s), f i = f a + ∑ᶠ (i : α) (_ : i ∈ s), f i

Given a finite set s and an element a ∉ s, the sum of f i over i ∈ insert a s equals f a plus the sum of f i over i ∈ s.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid