Theorems · Theorem · group theory
addOrderOf_nsmul_eq_zero
∀ {G : Type u_1} [inst : AddMonoid G] (x : G), addOrderOf x • x = 0- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 21 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.
Cites6
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
- Nat.iterateproof · cited by 740
- addOrderOfstatement and proof · cited by 208
- Function.minimalPeriodproof · cited by 100
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- add_left_iterate_apply_zeroproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- mod_addOrderOf_nsmulproof · cited by 7
- mod_addOrderOf_zsmulproof · cited by 3
- AddCircle.addOrderOf_eq_pos_iffproof · cited by 2
- AddAction.period_dvd_addOrderOfproof · cited by 2
- zsmul_smul_addOrderOfproof · cited by 2
- exists_addOrderOf_eq_prime_pow_iffproof · cited by 2
- neg_eq_self_of_addOrderOf_eq_twoproof · cited by 1
- addOrderOf_smul_dvdproof · cited by 1
- AddCommute.addOrderOf_dvd_lcm_addproof · cited by 1
- addOrderOf_map_dvdproof · cited by 1
- prime_dvd_char_iff_dvd_cardproof · cited by 1