Theorems · Theorem · group theory
AddSubmonoid.isOfFinAddOrder_coe
∀ {G : Type u_1} [inst : AddMonoid G] {H : AddSubmonoid G} {x : ↥H}, IsOfFinAddOrder ↑x ↔ IsOfFinAddOrder xElements of finite order are of finite order in submonoids.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- IsOfFinAddOrderstatement and proof · cited by 105
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- ZeroMemClass.coe_eq_zeroproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsAddTorsion.addSubgroupproof · cited by 1