Theorems · Theorem · number theory
HasEnoughRootsOfUnity.of_dvd
∀ (M : Type u_1) [inst : CommMonoid M] {m n : ℕ} [NeZero n],
m ∣ n → ∀ [HasEnoughRootsOfUnity M n], HasEnoughRootsOfUnity M mIf HasEnoughRootsOfUnity M n and m ∣ n, then also HasEnoughRootsOfUnity M m.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- IsPrimitiveRootproof · cited by 356
- NeZero.posproof · cited by 57
- HasEnoughRootsOfUnitystatement and proof · cited by 56
- IsPrimitiveRoot.powproof · cited by 8
- HasEnoughRootsOfUnity.exists_primitiveRootproof · cited by 5
- Subgroup.isCyclic_of_leproof · cited by 3
- rootsOfUnity_le_of_dvdproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- CommGroup.card_domRestrictHom_kerproof · cited by 2
- MonoidHom.domRestrict_surjectiveproof · cited by 2
- CommGroup.exists_apply_ne_one_of_hasEnoughRootsOfUnityproof · cited by 2
- CommGroup.monoidHom_mulEquiv_of_hasEnoughRootsOfUnityproof · cited by 2
- CommGroup.forall_monoidHom_apply_eq_one_iffproof · cited by 0