Theorems · Theorem · group theory
AddSubgroup.card_mul_index
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), Nat.card ↥H * H.index = Nat.card G- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 96 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nat.cardstatement and proof · cited by 844
- bot_leproof · cited by 306
- AddSubgroup.indexstatement and proof · cited by 104
- AddSubgroup.relIndexproof · cited by 67
- AddSubgroup.relIndex_mul_indexproof · cited by 12
- AddSubgroup.relIndex_bot_leftproof · cited by 4
- AddSubgroup.index_botproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- AddSubgroup.card_dvd_of_surjectiveproof · cited by 3
- AddSubgroup.index_mul_cardproof · cited by 2
- AddGroup.isAddCyclic_of_coprime_card_range_card_kerproof · cited by 1
- AddSubgroup.index_rangeproof · cited by 1
- AddSubgroup.finite_iff_finite_and_finiteIndexproof · cited by 1
- IsAddCyclic.card_nsmulAddMonoidHom_kerproof · cited by 1
- AddMonoidHom.surjective_of_card_ker_le_divproof · cited by 0