Theorems · Theorem · group theory
AddMonoid.exponent_nsmul_eq_zero
∀ {G : Type u} [inst : AddMonoid G] (g : G), AddMonoid.exponent G • g = 0- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 19 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.findproof · cited by 139
- zero_nsmulproof · cited by 137
- Nat.find_specproof · cited by 74
- AddMonoid.exponentstatement · cited by 70
- AddMonoid.ExponentExistsproof · cited by 17
Cited by12
Results whose statement or proof uses this declaration.
- AddMonoid.addOrder_dvd_exponentproof · cited by 10
- AddMonoidHom.exponent_dvdproof · cited by 4
- AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finiteproof · cited by 3
- AddMonoid.exponent_dvd_of_addMonoidHomproof · cited by 3
- AddAction.period_dvd_exponentproof · cited by 2
- AddMonoid.exp_eq_one_iffproof · cited by 2
- neg_eq_self_of_exponent_twoproof · cited by 1
- AddSubmonoid.nsmul_exponent_eq_zeroproof · cited by 1
- AddMonoid.nsmul_eq_mod_exponentproof · cited by 1
- add_notMem_of_exponent_twoproof · cited by 1
- Nat.Prime.exists_addOrderOf_eq_pow_padic_val_nat_add_exponentproof · cited by 1
- addOrderOf_eq_two_iffproof · cited by 0