Theorems · Theorem · group theory
QuotientAddGroup.subsingleton_iff
∀ {G : Type u_1} [inst : AddGroup G] {N : AddSubgroup G}, Subsingleton (G ⧸ N) ↔ N = ⊤- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 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.
Cites6
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
- HasQuotient.Quotientstatement · cited by 2,301
- Quotient.subsingleton_iffproof · cited by 2
- QuotientAddGroup.leftRel_eq_topproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.Quotient.subsingleton_iffproof · cited by 8
- QuotientAddGroup.subsingleton_quotient_topproof · cited by 1
- QuotientAddGroup.nontrivial_iffproof · cited by 1
- AddCommGroup.freeRank_eq_zero_iffproof · cited by 1