Theorems · Theorem · group theory
AddSubmonoid.multiples_le_zmultiples
∀ {G : Type u_2} [inst : AddGroup G] (g : G), AddSubmonoid.multiples g ≤ (AddSubgroup.zmultiples g).toAddSubmonoid- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubgroup.zmultiplesstatement · cited by 493
- le_sup_leftproof · cited by 265
- AddSubgroup.toAddSubmonoidstatement · cited by 91
- AddSubmonoid.multiplesstatement and proof · cited by 40
- AddSubgroup.toAddSubmonoid_zmultiplesproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- addOrderOf_eq_card_of_forall_mem_multiplesproof · cited by 0