Theorems · Theorem · group theory
addOrderOf_dvd_of_mem_zmultiples
∀ {G : Type u_1} [inst : AddGroup G] {x y : G}, y ∈ AddSubgroup.zmultiples x → addOrderOf y ∣ addOrderOf x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 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
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- addOrderOfstatement · cited by 208
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- AddSubgroup.mem_zmultiples_iffproof · cited by 11
- zsmul_smul_addOrderOfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1