Theorems · Theorem · group theory
Associated.map
∀ {M : Type u_2} {N : Type u_3} [inst : Monoid M] [inst_1 : Monoid N] {F : Type u_4} [inst_2 : FunLike F M N]
[MonoidHomClass F M N] (f : F) {x y : M}, Associated x y → Associated (f x) (f y)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
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.
- DFunLike.coestatement and proof · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- Unitsproof · cited by 2,804
- FunLikestatement and proof · cited by 2,560
- Units.valproof · cited by 1,966
- map_mulproof · cited by 1,137
- Associatedstatement and proof · cited by 296
- MonoidHomClass.toMonoidHomproof · cited by 294
- MonoidHomClassstatement and proof · cited by 244
- Units.mapproof · cited by 95
- Units.coe_mapproof · cited by 7
- MonoidHom.coe_coeproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.associated_primPart_mulproof · cited by 2
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_powproof · cited by 1
- Polynomial.associated_map_mapproof · cited by 0
- Polynomial.Separable.map_irreducible_of_isPurelyInseparableproof · cited by 0