Theorems · Theorem · group theory
Subgroup.card_dvd_of_le
∀ {α : Type u_1} [inst : Group α] {H K : Subgroup α}, H ≤ K → Nat.card ↥H ∣ Nat.card ↥K- Defined in
- Mathlib.GroupTheory.Coset.Card
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Nat.cardstatement · cited by 844
- Subgroup.inclusionproof · cited by 21
- Subgroup.inclusion_injectiveproof · cited by 4
- Subgroup.card_dvd_of_injectiveproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.disjoint_of_coprime_natCardproof · cited by 3
- isZGroup_of_coprimeproof · cited by 1
- Sylow.not_dvd_card_commutator_or_not_dvd_index_commutatorproof · cited by 1
- Subgroup.card_comap_dvd_of_injectiveproof · cited by 0
- MonoidHom.ker_transferSylow_disjointproof · cited by 0