Theorems · Theorem · group theory

Finset.sum_comp

∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} {s : Finset ι} [inst : AddCommMonoid M] [inst_1 : DecidableEq κ]
  (f : κ → M) (g : ι → κ), ∑ a ∈ s, f (g a) = ∑ b ∈ Finset.image g s, {a ∈ s | g a = b}.card • f b

The sum of the composition of functions f and g, is the sum over b ∈ s.image g of f b times of the cardinality of the fibre of b. See also Finset.sum_image.

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Basic

Cited by

4 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidDecidableEq