Theorems · Theorem · group theory
AddSubgroup.index_eq_card
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), H.index = Nat.card (G ⧸ H)- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 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.
Cites5
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.Quotientstatement · cited by 2,301
- Nat.cardstatement · cited by 844
- AddSubgroup.indexstatement · cited by 104
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.index_ne_zero_of_finiteproof · cited by 4
- AddSubgroup.exists_finset_card_le_addproof · cited by 0