Theorems · Theorem · group theory
AddSubgroup.finite_iff_finite_and_finiteIndex
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), Finite G ↔ Finite ↥H ∧ H.FiniteIndex- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Finitestatement and proof · cited by 3,029
- LT.lt.ne'proof · cited by 1,417
- mul_ne_zeroproof · cited by 178
- AddSubgroup.FiniteIndexstatement and proof · cited by 66
- Nat.card_posproof · cited by 36
- Nat.finite_of_card_ne_zeroproof · cited by 33
- AddSubgroup.FiniteIndex.index_ne_zeroproof · cited by 10
- AddSubgroup.card_mul_indexproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoidHom.finite_iff_finite_ker_rangeproof · cited by 1