Theorems · Theorem · group theory
QuotientAddGroup.leftRel_eq_top
∀ {G : Type u_1} [inst : AddGroup G] {N : AddSubgroup G}, QuotientAddGroup.leftRel N = ⊤ ↔ N = ⊤- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- zero_addproof · cited by 2,366
- neg_zeroproof · cited by 542
- AddOppositeproof · cited by 452
- AddOpposite.unopproof · cited by 125
- AddAction.orbitproof · cited by 86
- AddSubgroup.extproof · cited by 75
- AddSubgroup.opproof · cited by 57
- QuotientAddGroup.leftRelstatement · cited by 34
- AddSubgroup.mem_topproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- QuotientAddGroup.subsingleton_iffproof · cited by 4