Theorems · Theorem · group theory
Subgroup.relIndex_mul_index
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H ≤ K → H.relIndex K * K.index = H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 94 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.
Cites10
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
- HasQuotient.Quotientproof · cited by 2,301
- mul_commproof · cited by 2,262
- Nat.cardproof · cited by 844
- Subgroup.indexstatement and proof · cited by 150
- Nat.card_congrproof · cited by 133
- Subgroup.subgroupOfproof · cited by 122
- Subgroup.relIndexstatement and proof · cited by 72
- Subgroup.quotientEquivProdOfLEproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- Subgroup.card_mul_indexproof · cited by 16
- Subgroup.index_dvd_of_leproof · cited by 8
- Subgroup.index_mapproof · cited by 6
- Subgroup.relIndex_top_rightproof · cited by 6
- MulAction.IsBlock.ncard_block_mul_ncard_orbit_eqproof · cited by 4
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Subgroup.relIndex_mul_relIndexproof · cited by 2
- NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndexproof · cited by 2
- Subgroup.relIndex_dvd_index_of_leproof · cited by 2
- Sylow.not_dvd_index'proof · cited by 1
- NumberField.Units.regOfFamily_div_regOfFamilyproof · cited by 1
- Ideal.ncard_primesOver_mul_ncard_primesOverproof · cited by 0