Theorems · Theorem · group theory

MonoidWithZeroHom.one_apply_apply_eq

∀ {M₀ : Type u_1} {N₀ : Type u_2} {G₀ : Type u_3} [inst : GroupWithZero M₀] [inst_1 : MulZeroOneClass N₀]
  [inst_2 : Nontrivial N₀] [inst_3 : NoZeroDivisors N₀] [inst_4 : MulZeroOneClass G₀]
  [inst_5 : DecidablePred fun x => x = 0] [inst_6 : DecidablePred fun x => x = 0] (f : M₀ →*₀ N₀) (x : M₀),
  1 (f x) = 1 x

The trivial group-with-zero hom is absorbing for composition.

Defined in

Mathlib.Algebra.GroupWithZero.ProdHom

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupWithZeroMulZeroOneClassNontrivialNoZeroDivisorsMulZeroOneClassDecidablePredDecidablePred