Theorems · Theorem · group theory

MonoidHom.map_finprod_mem

∀ {α : Type u_1} {M : Type u_5} {N : Type u_6} [inst : CommMonoid M] [inst_1 : CommMonoid N] {s : Set α} (f : α → M)
  (g : M →* N), s.Finite → g (∏ᶠ (j : α) (_ : j ∈ s), f j) = ∏ᶠ (i : α) (_ : i ∈ s), g (f i)

Given a monoid homomorphism g : M →* N and a function f : α → M, the value of g at the product of f i over i ∈ s equals the product of g (f i) over s.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoid