Theorems · Definition · group theory
Subgroup.quotientEquivOfEq
{α : Type u_1} → [inst : Group α] → {s t : Subgroup α} → s = t → α ⧸ s ≃ α ⧸ tIf two subgroups M and N of G are equal, their quotients are in bijection.
- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Quotient.map'proof · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- QuotientGroup.quotientMulEquivOfEqproof · cited by 5
- Subgroup.quotientCenterEmbeddingproof · cited by 2
- Subgroup.quotientCentralizerEmbeddingproof · cited by 1
- Subgroup.quotientEquivOfEq_mkstatement · cited by 0
- MulAction.selfEquivOrbitsQuotientProd'proof · cited by 0
- Subgroup.quotientIsometryEquivOfEqproof · cited by 0