Theorems · Theorem · group theory
Subgroup.index_antitone
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H ≤ K → ∀ [H.FiniteIndex], K.index ≤ H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 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.indexstatement · cited by 150
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.FiniteIndex.index_ne_zeroproof · cited by 12
- Subgroup.index_dvd_of_leproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1
- Subgroup.index_strictAntiproof · cited by 0