Theorems · Theorem · group theory
AddMonoid.addOrder_dvd_exponent
∀ {G : Type u} [inst : AddMonoid G] (g : G), addOrderOf g ∣ AddMonoid.exponent G- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 32 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.
Cites5
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
- addOrderOfstatement · cited by 208
- AddMonoid.exponentstatement · cited by 70
- AddMonoid.exponent_nsmul_eq_zeroproof · cited by 12
- addOrderOf_dvd_of_nsmul_eq_zeroproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- IsAddCyclic.exponent_eq_cardproof · cited by 5
- AddMonoid.ExponentExists.of_finiteproof · cited by 2
- AddMonoid.addOrderOf_le_exponentproof · cited by 1
- AddMonoid.exponent_prodproof · cited by 1
- AddMonoid.exists_addOrderOf_eq_exponentproof · cited by 1
- add_comm_of_exponent_twoproof · cited by 1
- AddMonoid.exponent_eq_prime_iffproof · cited by 1
- card_dvd_exponent_nsmul_rankproof · cited by 1
- AddMonoid.lcm_addOrderOf_dvd_exponentproof · cited by 1
- AddMonoid.exponent_piproof · cited by 0