Theorems · Theorem · group theory
AddSubmonoid.subsingleton_iff
∀ {M : Type u_1} [inst : AddZeroClass M], Subsingleton (AddSubmonoid M) ↔ Subsingleton M- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- ZeroMemClass.zero_memproof · cited by 162
- AddSubmonoid.extproof · cited by 32
- AddSubmonoid.mem_topproof · cited by 20
- AddSubmonoid.mem_botproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.subsingleton_iffproof · cited by 7
- AddSubmonoid.nontrivial_iffproof · cited by 0