Theorems · Theorem · group theory
AddSubgroup.index_ne_zero_of_finite
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} [hH : Finite (G ⧸ H)], H.index ≠ 0- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fintypeproof · cited by 7,736
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- LT.lt.ne'proof · cited by 1,417
- nonempty_fintypeproof · cited by 261
- AddSubgroup.indexstatement · cited by 104
- Nat.card_posproof · cited by 36
- AddSubgroup.index_eq_cardproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.finiteIndex_of_finite_quotientproof · cited by 7
- Submodule.finite_quotient_smulproof · cited by 2
- IsAddCyclic.card_nsmulAddMonoidHom_kerproof · cited by 1
- AddSubgroup.one_lt_index_of_ne_topproof · cited by 0