Theorems · Theorem · group theory
Subgroup.relIndex_inf_ne_zero
∀ {G : Type u_1} [inst : Group G] {H K L : Subgroup G}, H.relIndex L ≠ 0 → K.relIndex L ≠ 0 → (H ⊓ K).relIndex L ≠ 0- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- inf_le_rightproof · cited by 238
- Subgroup.relIndexstatement and proof · cited by 72
- inf_assocproof · cited by 53
- Subgroup.inf_relIndex_rightproof · cited by 8
- Subgroup.relIndex_eq_zero_of_le_rightproof · cited by 5
- Subgroup.relIndex_ne_zero_transproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.index_inf_ne_zeroproof · cited by 0