Theorems · Definition · group theory
Subgroup.quotientSubgroupOfEmbeddingOfLE
{α : Type u_1} →
[inst : Group α] → {s t : Subgroup α} → (H : Subgroup α) → s ≤ t → ↥s ⧸ H.subgroupOf s ↪ ↥t ⧸ H.subgroupOf tIf s ≤ t, then there is an embedding s ⧸ H.subgroupOf s ↪ t ⧸ H.subgroupOf t.
- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 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.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Function.Embeddingstatement · cited by 988
- Subgroup.subgroupOfstatement · cited by 122
- Subgroup.inclusionproof · cited by 21
- Quotient.map'proof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.relIndex_eq_zero_of_le_rightproof · cited by 5
- Subgroup.relIndex_le_of_le_rightproof · cited by 1
- Subgroup.quotientSubgroupOfEmbeddingOfLE_apply_mkstatement · cited by 0