Theorems · Theorem · group theory
orderOf_pos
∀ {G : Type u_1} [inst : LeftCancelMonoid G] [Finite G] (x : G), 0 < orderOf xThis is the same as IsOfFinOrder.orderOf_pos but with one fewer explicit assumption since this
is automatic in case of a finite cancellative monoid.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoidFinite
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.
- Finitestatement and proof · cited by 3,029
- orderOfstatement · cited by 324
- LeftCancelMonoidstatement and proof · cited by 28
- IsOfFinOrder.orderOf_posproof · cited by 17
- isOfFinOrder_of_finiteproof · cited by 14
Cited by15
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.exists_pow_eqproof · cited by 7
- map_rootsOfUnity_eq_pow_selfproof · cited by 3
- Equiv.Perm.SameCycle.exists_pow_eq'proof · cited by 3
- QuaternionGroup.orderOf_a_oneproof · cited by 2
- DihedralGroup.orderOf_r_oneproof · cited by 2
- ZMod.isCyclic_units_of_prime_powproof · cited by 2
- Monoid.ExponentExists.of_finiteproof · cited by 2
- sum_hom_units_eq_zeroproof · cited by 1
- Monoid.exponent_eq_max'_orderOfproof · cited by 1
- Equiv.Perm.isCycle_of_prime_orderproof · cited by 1
- Equiv.Perm.isCycle_of_prime_order''proof · cited by 1
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1