Theorems · Theorem · group theory
AddSubgroup.index_mul_card
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), H.index * Nat.card ↥H = Nat.card G- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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.
Cites6
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
- mul_commproof · cited by 2,262
- Nat.cardstatement and proof · cited by 844
- AddSubgroup.indexstatement and proof · cited by 104
- AddSubgroup.card_mul_indexproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.index_rangeproof · cited by 1
- AddSubgroup.index_dvd_cardproof · cited by 1