Theorems · Theorem · group theory
AddSubgroup.finiteIndex_of_finite_quotient
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} [Finite (G ⧸ H)], H.FiniteIndex- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AddSubgroup.FiniteIndexstatement · cited by 66
- AddSubgroup.index_ne_zero_of_finiteproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- AddSubgroup.IsComplement.finite_left_iffproof · cited by 3
- AddSubgroup.finiteIndex_of_leftCoset_cover_constproof · cited by 2
- AddSubgroup.finiteIndex_iff_finite_quotientproof · cited by 2
- Ideal.isOpen_of_isMaximalproof · cited by 1
- Ideal.isOpen_pow_of_isMaximalproof · cited by 1
- AddSubgroup.IsComplement.finite_right_iffproof · cited by 1