Theorems · Theorem · group theory
MonoidWithZeroHom.one_apply_eq_zero_iff
∀ {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] [Nontrivial N₀]
{x : M₀}, 1 x = 0 ↔ x = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Hom
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Nontrivialstatement and proof · cited by 2,416
- eq_or_neproof · cited by 1,117
- MonoidWithZeroHomstatement · cited by 704
- NoZeroDivisorsstatement and proof · cited by 545
- MulZeroOneClassstatement and proof · cited by 184
- MonoidWithZeroHom.one_apply_of_ne_zeroproof · cited by 7
- MonoidWithZeroHom.one_apply_zeroproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.one_apply_eq_zero_iffproof · cited by 0