Theorems · Theorem · group theory
Associated.eq_zero_iff
∀ {M : Type u_1} [inst : MonoidWithZero M] {a b : M}, Associated a b → (a = 0 ↔ b = 0)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Units.eq_mul_inv_iff_mul_eqproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Associated.ne_zero_iffproof · cited by 3
- UniqueFactorizationMonoid.factors_rel_of_associatedproof · cited by 2