Theorems · Theorem · group theory
addOrderOf_pos_iff
∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, 0 < addOrderOf x ↔ IsOfFinAddOrder xA group element has finite additive order iff its order is positive.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- addOrderOfstatement and proof · cited by 208
- pos_iff_ne_zeroproof · cited by 180
- IsOfFinAddOrderstatement · cited by 105
- iff_not_commproof · cited by 16
- addOrderOf_eq_zero_iffproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- finite_zmultiplesproof · cited by 3
- AddCircle.gcd_mul_addOrderOf_div_eqproof · cited by 3
- Function.Injective.isOfFinAddOrder_iffproof · cited by 2
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- IsOfFinAddOrder.monoproof · cited by 2
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- AddCommute.isOfFinAddOrder_addproof · cited by 1
- approxAddOrderOf.vadd_eq_of_mul_dvdproof · cited by 1
- AddCircle.le_add_order_smul_norm_of_isOfFinAddOrderproof · cited by 1
- IsOfFinAddOrder.prod_mkproof · cited by 1