Theorems · Theorem · group theory
associated_zero_iff_eq_zero
∀ {M : Type u_1} [inst : MonoidWithZero M] (a : M), Associated a 0 ↔ a = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- MulZeroClass.zero_mulproof · cited by 1,625
- MonoidWithZerostatement and proof · cited by 456
- Associatedstatement and proof · cited by 296
- Associated.symmproof · cited by 87
- Associated.reflproof · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- Associates.mk_eq_zeroproof · cited by 6
- normalize_eq_zeroproof · cited by 1
- lcm_eq_zero_iffproof · cited by 0
- Associates.factors'_congproof · cited by 0