Theorems · Theorem · group theory
AddMonoid.addOrderOf_eq_one_iff
∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, addOrderOf x = 1 ↔ x = 0- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 22 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
- add_zeroproof · cited by 2,707
- addOrderOfstatement · cited by 208
- Function.minimalPeriod_eq_one_iff_isFixedPtproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- CharacterModule.eq_zero_of_ofSpanSingleton_apply_selfproof · cited by 1
- prime_dvd_char_iff_dvd_cardproof · cited by 1
- AddMonoid.exponent_eq_prime_iffproof · cited by 1
- not_isAddCyclic_iff_exponent_eq_primeproof · cited by 0
- AddCommMonoid.primaryComponent.disjointproof · cited by 0
- exists_nsmul_eq_self_of_coprimeproof · cited by 0