Theorems · Definition · group theory
AddSubgroup.quotientAddSubgroupOfMapOfLE
{α : Type u_1} →
[inst : AddGroup α] →
{s t : AddSubgroup α} → (H : AddSubgroup α) → s ≤ t → ↥H ⧸ s.addSubgroupOf H → ↥H ⧸ t.addSubgroupOf HIf s ≤ t, then there is a map H ⧸ s.addSubgroupOf H → H ⧸ t.addSubgroupOf H.
- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- AddSubgroup.addSubgroupOfstatement · cited by 87
- Quotient.map'proof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.quotientiInfAddSubgroupOfEmbeddingproof · cited by 4
- AddSubgroup.quotientAddSubgroupOfMapOfLE_apply_mkstatement · cited by 0
- AddSubgroup.quotientiInfAddSubgroupOfEmbedding_applystatement · cited by 0