Theorems · Theorem · group theory
isOfFinAddOrder_of_finite
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] [Finite G] (x : G), IsOfFinAddOrder x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddLeftCancelMonoidFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- Finitestatement and proof · cited by 3,029
- Set.toFiniteproof · cited by 174
- IsOfFinAddOrderstatement and proof · cited by 105
- AddLeftCancelMonoidstatement and proof · cited by 37
- infinite_not_isOfFinAddOrderproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- addOrderOf_posproof · cited by 3
- Fintype.card_zmultiplesproof · cited by 3
- mem_multiples_iff_mem_zmultiplesproof · cited by 3
- addOrderOf_nsmulproof · cited by 2
- mem_zmultiples_iff_mem_range_addOrderOfproof · cited by 1
- multiplesEquivMultiplesproof · cited by 1
- multiples_eq_zmultiplesproof · cited by 0
- exists_zsmul_eq_zeroproof · cited by 0
- addOrderOf_eq_card_multiplesproof · cited by 0
- AddSubgroup.closure_toAddSubmonoid_of_finiteproof · cited by 0
- multiplesEquivMultiples_applyproof · cited by 0