Theorems · Definition · group theory
QuotientAddGroup.rightRel
{α : Type u_1} → [inst : AddGroup α] → AddSubgroup α → Setoid αThe equivalence relation corresponding to the partition of a group by right cosets of a subgroup.
- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 66 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.
Cites3
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
- AddAction.orbitRelproof · cited by 47
Cited by16
Results whose statement or proof uses this declaration.
- QuotientAddGroup.rightRel_applystatement · cited by 6
- AddSubgroup.IsComplement.rightQuotientEquivstatement · cited by 5
- AddSubgroup.exists_isComplement_rightproof · cited by 3
- QuotientAddGroup.quotientRightRelEquivQuotientLeftRelstatement · cited by 3
- AddSubgroup.isComplement_addSubgroup_left_iff_bijectivestatement · cited by 2
- AddSubgroup.isComplement_range_rightstatement and proof · cited by 2
- AddSubgroup.isComplement_addSubgroup_left_iff_existsUnique_quotientMk''statement and proof · cited by 1
- QuotientAddGroup.card_quotient_rightRelstatement · cited by 1
- AddSubgroup.IsComplement.mk''_rightQuotientEquivstatement and proof · cited by 1
- ProperlyDiscontinuousVAdd.ofFiniteRelIndexproof · cited by 1
- QuotientAddGroup.rightRel_eqstatement · cited by 0
- QuotientAddGroup.rightRel_eq_topstatement · cited by 0