Theorems · Theorem · group theory

MonoidHom.map_finprod_of_preimage_one

∀ {M : Type u_2} {N : Type u_3} {α : Sort u_4} [inst : CommMonoid M] [inst_1 : CommMonoid N] (f : M →* N),
  (∀ (x : M), f x = 1 → x = 1) → ∀ (g : α → M), f (∏ᶠ (i : α), g i) = ∏ᶠ (i : α), f (g i)

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

2 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoid