Theorems · Theorem · group theory
AddMonoidHom.map_zmultiples
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_3} [inst_1 : AddGroup N] (f : G →+ N) (x : G),
AddSubgroup.map f (AddSubgroup.zmultiples x) = AddSubgroup.zmultiples (f x)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Setproof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- AddSubgroup.mapstatement and proof · cited by 189
- Set.image_singletonproof · cited by 174
- AddSubgroup.closureproof · cited by 156
- AddSubgroup.zmultiples_eq_closureproof · cited by 9
- AddMonoidHom.map_closureproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_topproof · cited by 4
- CongruenceSubgroup.strictPeriods_Gammaproof · cited by 2
- IsAddCyclic.card_nsmulAddMonoidHom_rangeproof · cited by 1
- AddCircle.denseRange_zsmul_coe_iffproof · cited by 0
- AddCircle.dense_addSubgroup_iff_ne_zmultiplesproof · cited by 0
- Int.addEquiv_eq_refl_or_negproof · cited by 0