Theorems · Theorem · group theory
AddSubgroup.relIndex_iInf_ne_zero
∀ {G : Type u_1} [inst : AddGroup G] {L : AddSubgroup G} {ι : Type u_3} [_hι : Finite ι] {f : ι → AddSubgroup G},
(∀ (i : ι), (f i).relIndex L ≠ 0) → (⨅ i, f i).relIndex L ≠ 0- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finset.univproof · cited by 3,473
- AddSubgroupstatement and proof · cited by 3,232
- Finitestatement and proof · cited by 3,029
- iInfstatement · cited by 1,690
- AddSubgroup.relIndexstatement and proof · cited by 67
- Finset.prod_ne_zero_iffproof · cited by 45
- Nat.card_piproof · cited by 10
- Finite.card_eq_zero_of_embeddingproof · cited by 4
- AddSubgroup.quotientiInfAddSubgroupOfEmbeddingproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.index_iInf_ne_zeroproof · cited by 1