Theorems · Theorem · group theory
Subgroup.finiteIndex_of_le
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G} [H.FiniteIndex], H ≤ K → K.FiniteIndex- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.FiniteIndex
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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.FiniteIndexstatement and proof · cited by 113
- ne_zero_of_dvd_ne_zeroproof · cited by 26
- Subgroup.FiniteIndex.index_ne_zeroproof · cited by 12
- Subgroup.index_dvd_of_leproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndexproof · cited by 2
- Subgroup.isFiniteRelIndex_of_le_leftproof · cited by 1
- CongruenceSubgroup.IsCongruenceSubgroup.finiteIndexproof · cited by 0