Theorems · Theorem · group theory
IsOfFinAddOrder.addOrderOf_pos
∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, IsOfFinAddOrder x → 0 < addOrderOf x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 20 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.
Cites4
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 · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- Function.minimalPeriod_pos_of_mem_periodicPtsproof · cited by 9
Cited by16
Results whose statement or proof uses this declaration.
- addOrderOf_eq_zero_iffproof · cited by 9
- IsOfFinAddOrder.mem_multiples_iff_mem_zmultiplesproof · cited by 4
- addOrderOf_posproof · cited by 3
- IsOfFinAddOrder.mem_multiples_iff_mem_range_addOrderOfproof · cited by 2
- finEquivMultiples_symm_applystatement and proof · cited by 2
- AddCommute.addOrderOf_add_eq_right_of_forall_prime_mul_dvdproof · cited by 2
- AddMonoid.ExponentExists.addOrderOf_posproof · cited by 2
- AddCircle.exists_gcd_eq_one_of_isOfFinAddOrderproof · cited by 1
- AddCommute.isOfFinAddOrder_addproof · cited by 1
- IsOfFinAddOrder.zsmulproof · cited by 1
- finEquivZMultiples_symm_applystatement and proof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1