Theorems · Theorem · group theory
orderOf_eq_zero_iff
∀ {G : Type u_1} [inst : Monoid G] {x : G}, orderOf x = 0 ↔ ¬IsOfFinOrder x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 22 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.
Cites6
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
- LT.lt.ne'proof · cited by 1,417
- orderOfstatement and proof · cited by 324
- IsOfFinOrderstatement and proof · cited by 113
- IsOfFinOrder.orderOf_posproof · cited by 17
- orderOf_eq_zeroproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- orderOf_pos_iffproof · cited by 8
- RightCancelMonoid.injective_pow_iff_not_isOfFinOrderproof · cited by 1
- injective_zpow_iff_not_isOfFinOrderproof · cited by 1
- injective_pow_iff_not_isOfFinOrderproof · cited by 1
- Polynomial.irreducible_of_dvd_cyclotomic_of_natDegreeproof · cited by 1
- orderOf_ne_zero_iffproof · cited by 0
- IsMulTorsionFree.orderOf_le_oneproof · cited by 0
- orderOf_zeroproof · cited by 0