Theorems · Theorem · group theory
IsOfFinOrder.orderOf_pos
∀ {G : Type u_1} [inst : Monoid G] {x : G}, IsOfFinOrder x → 0 < orderOf x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- orderOfstatement · cited by 324
- IsOfFinOrderstatement and proof · cited by 113
- Function.minimalPeriod_pos_of_mem_periodicPtsproof · cited by 9
Cited by17
Results whose statement or proof uses this declaration.
- orderOf_posproof · cited by 15
- orderOf_eq_zero_iffproof · cited by 8
- IsOfFinOrder.mem_powers_iff_mem_zpowersproof · cited by 4
- MulChar.orderOf_posproof · cited by 3
- minpoly_algEquiv_toLinearMapproof · cited by 2
- orderOf_eq_of_pow_and_pow_div_primeproof · cited by 2
- Monoid.ExponentExists.orderOf_posproof · cited by 2
- finEquivPowers_symm_applystatement and proof · cited by 2
- IsOfFinOrder.mem_powers_iff_mem_range_orderOfproof · cited by 2
- Commute.orderOf_mul_eq_right_of_forall_prime_mul_dvdproof · cited by 2
- IsOfFinOrder.zpowproof · cited by 1
- isPrimitiveRoot_of_mem_rootsOfUnityproof · cited by 1