Theorems · Theorem · group theory
Associates.mk_dvd_mk
∀ {M : Type u_1} [inst : CommMonoid M] {a b : M}, Associates.mk a ∣ Associates.mk b ↔ a ∣ b- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidproof · cited by 3,887
- Unitsproof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- Associatedproof · cited by 296
- Associatesstatement and proof · cited by 210
- Associates.mkstatement and proof · cited by 137
- Function.Surjective.existsproof · cited by 53
- Associated.reflproof · cited by 25
- Associates.mk_surjectiveproof · cited by 7
- Associated.commproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- Ideal.count_associates_factors_eqproof · cited by 4
- Associates.mk_le_mk_iff_dvdproof · cited by 4
- Associates.mk_le_mk_of_dvdproof · cited by 3
- Ideal.torsionOf_eq_span_pow_pOrderproof · cited by 2
- Associates.dvd_of_mk_le_mkproof · cited by 1
- Ideal.finprod_countproof · cited by 1
- mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactorsproof · cited by 1
- Associates.mem_factors'_iff_dvdproof · cited by 0
- Associates.mem_factors_iff_dvdproof · cited by 0