Theorems · Definition · group theory
AddSubmonoid.multiples
{A : Type u_2} → [inst : AddMonoid A] → A → AddSubmonoid AThe additive submonoid generated by an element.
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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.
- DFunLike.coeproof · cited by 62,936
- Set.rangeproof · cited by 4,705
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- AddMonoidHom.mrangeproof · cited by 61
- multiplesHomproof · cited by 5
- AddSubmonoid.copyproof · cited by 3
Cited by48
Results whose statement or proof uses this declaration.
- finEquivMultiplesstatement · cited by 7
- AddSubmonoid.multiples_lestatement · cited by 4
- IsOfFinAddOrder.mem_multiples_iff_mem_zmultiplesstatement and proof · cited by 4
- IsOfFinAddOrder.finite_multiplesstatement · cited by 3
- AddSubmonoid.multiples_eq_closurestatement · cited by 3
- mem_multiples_iff_mem_zmultiplesstatement · cited by 3
- AddSubmonoid.mem_multiples_iffstatement · cited by 2
- finEquivMultiples_symm_applystatement and proof · cited by 2
- IsOfFinAddOrder.mem_multiples_iff_mem_range_addOrderOfstatement · cited by 2
- IsOfFinAddOrder.multiples_eq_image_range_addOrderOfstatement · cited by 2
- IsOfFinAddOrder.multiples_eq_zmultiplesstatement · cited by 2
- AddSubmonoid.LocalizationMap.AwayMapproof · cited by 2