Theorems · Theorem · group theory
AddMonoid.exponent_dvd_iff_forall_nsmul_eq_zero
∀ {G : Type u} [inst : AddMonoid G] {n : ℕ}, AddMonoid.exponent G ∣ n ↔ ∀ (g : G), n • g = 0- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 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.
Cites9
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
- LT.lt.not_geproof · cited by 305
- pos_iff_ne_zeroproof · cited by 180
- zero_nsmulproof · cited by 137
- AddMonoid.exponentstatement and proof · cited by 70
- dvd_zeroproof · cited by 63
- AddMonoid.exponent_min'proof · cited by 3
- AddMonoid.exponent_pos_of_existsproof · cited by 2
- AddMonoid.nsmul_eq_mod_exponentproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_dvdproof · cited by 5
- AddMonoid.exponent_dvd_of_forall_nsmul_eq_zeroproof · cited by 5
- AddGroup.exponent_dvd_iff_forall_zsmul_eq_zeroproof · cited by 1
- Nat.Prime.exists_addOrderOf_eq_pow_padic_val_nat_add_exponentproof · cited by 1