Theorems · Definition · group theory
Subgroup.IsComplement.rightQuotientEquiv
{G : Type u_1} →
[inst : Group G] →
{H : Subgroup G} → {T : Set G} → Subgroup.IsComplement (↑H) T → Quotient (QuotientGroup.rightRel H) ≃ ↑TA right transversal is in bijection with right cosets.
- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 72 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Equiv.symmproof · cited by 3,681
- Subgroupstatement and proof · cited by 3,593
- Set.domRestrictproof · cited by 383
- Quotient.mk''proof · cited by 132
- Subgroup.IsComplementstatement and proof · cited by 94
- Equiv.ofBijectiveproof · cited by 70
- QuotientGroup.rightRelstatement · cited by 44
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.toRightFunproof · cited by 8
- Subgroup.IsComplement.finite_right_iffproof · cited by 1
- ProperlyDiscontinuousSMul.ofFiniteRelIndexproof · cited by 1
- Subgroup.exists_finset_card_le_mulproof · cited by 1
- Subgroup.IsComplement.mk''_rightQuotientEquivstatement and proof · cited by 1
- Subgroup.IsComplement.rightQuotientEquiv_applystatement and proof · cited by 0