Theorems · Theorem · group theory

Finset.prod_erase

∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] [inst_1 : DecidableEq ι] (s : Finset ι) {f : ι → M} {a : ι},
  f a = 1 → ∏ x ∈ s.erase a, f x = ∏ x ∈ s, f x

If a function applied at a point is 1, a product is unchanged by removing that point, if present, from a Finset.

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Basic

Cited by

2 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidDecidableEq