Theorems · Theorem · group theory
AddSubgroup.relIndex_mul_index
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G}, H ≤ K → H.relIndex K * K.index = H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientproof · cited by 2,301
- mul_commproof · cited by 2,262
- Nat.cardproof · cited by 844
- Nat.card_congrproof · cited by 133
- AddSubgroup.indexstatement and proof · cited by 104
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.relIndexstatement and proof · cited by 67
- Nat.card_prodproof · cited by 24
- AddSubgroup.quotientEquivProdOfLEproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- AddSubgroup.card_mul_indexproof · cited by 7
- AddSubgroup.relIndex_top_rightproof · cited by 7
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqproof · cited by 4
- AddSubgroup.index_mapproof · cited by 3
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- AddSubgroup.index_dvd_of_leproof · cited by 3
- AddSubgroup.relIndex_mul_relIndexproof · cited by 2
- Submodule.finite_quotient_smulproof · cited by 2
- Submodule.index_smul_leproof · cited by 1
- AddSubgroup.relIndex_dvd_index_of_leproof · cited by 1
- AddSubgroup.index_strictAntiproof · cited by 0