Theorems · Theorem · group theory
Subgroup.index_dvd_of_le
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H ≤ K → K.index ∣ H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 95 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
- Subgroup.indexstatement · cited by 150
- Subgroup.relIndexproof · cited by 72
- Subgroup.relIndex_mul_indexproof · cited by 14
- dvd_of_mul_left_eqproof · cited by 14
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.finiteIndex_of_leproof · cited by 3
- Subgroup.index_map_dvdproof · cited by 2
- Subgroup.index_antitoneproof · cited by 2
- IsPGroup.indexproof · cited by 1
- NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvdproof · cited by 1
- Sylow.not_dvd_card_commutator_or_not_dvd_index_commutatorproof · cited by 1
- Sylow.card_dvd_indexproof · cited by 0
- Subgroup.normal_of_index_eq_minFac_cardproof · cited by 0