Theorems · Theorem · group theory
Subgroup.quotientiInfSubgroupOfEmbedding_apply
∀ {α : Type u_1} [inst : Group α] {ι : Type u_2} (f : ι → Subgroup α) (H : Subgroup α)
(q : ↥H ⧸ (⨅ i, f i).subgroupOf H) (i : ι),
(Subgroup.quotientiInfSubgroupOfEmbedding f H) q i = Subgroup.quotientSubgroupOfMapOfLE H ⋯ q- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- iInfstatement and proof · cited by 1,690
- Function.Embeddingstatement · cited by 988
- Subgroup.subgroupOfstatement and proof · cited by 122
- Subgroup.quotientiInfSubgroupOfEmbeddingstatement and proof · cited by 4
- Subgroup.quotientSubgroupOfMapOfLEstatement · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.