Theorems · Theorem · group theory
AddSubgroup.toAddSubmonoid_zmultiples
∀ {G : Type u_2} [inst : AddGroup G] (g : G),
(AddSubgroup.zmultiples g).toAddSubmonoid = AddSubmonoid.multiples g ⊔ AddSubmonoid.multiples (-g)- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupproof · cited by 3,232
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubgroup.zmultiplesstatement · cited by 493
- AddSubmonoid.closureproof · cited by 224
- AddSubgroup.toAddSubmonoidstatement and proof · cited by 91
- AddSubmonoid.multiplesstatement and proof · cited by 40
- Set.neg_singletonproof · cited by 14
- AddSubmonoid.closure_unionproof · cited by 10
- AddSubgroup.zmultiples_eq_closureproof · cited by 9
- AddSubgroup.closure_toAddSubmonoidproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.multiples_le_zmultiplesproof · cited by 1