Theorems · Theorem · group theory

MonoidWithZeroHom.one_apply_of_ne_zero

∀ {M₀ : Type u_7} {N₀ : Type u_8} [inst : MulZeroOneClass M₀] [inst_1 : MulZeroOneClass N₀]
  [inst_2 : DecidablePred fun x => x = 0] [inst_3 : Nontrivial M₀] [inst_4 : NoZeroDivisors M₀] {x : M₀},
  x ≠ 0 → 1 x = 1

Defined in

Mathlib.Algebra.GroupWithZero.Hom

Cited by

7 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext

Assumes

MulZeroOneClassMulZeroOneClassDecidablePredNontrivialNoZeroDivisors