Theorems · Theorem · order theory
Set.not_subsingleton_iff
∀ {α : Type u} {s : Set α}, ¬s.Subsingleton ↔ s.Nontrivial- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.Subsingletonstatement · cited by 276
- Set.Nontrivialstatement · cited by 145
Cited by7
Results whose statement or proof uses this declaration.
- Set.not_nontrivial_iffproof · cited by 13
- Set.Nontrivial.not_subsingletonproof · cited by 5
- Set.one_lt_ncard_iff_nontrivialproof · cited by 3
- vectorSpan_eq_bot_iff_subsingletonproof · cited by 1
- IsPreconnected.infinite_of_nontrivialproof · cited by 1
- Topology.CWComplex.OneSkeletonGraph.not_exists_isLoopAt_iff_nontrivialproof · cited by 0
- Set.Infinite.nontrivialproof · cited by 0