Theorems · Theorem · order theory
Set.singleton_ne_univ
∀ {α : Type u} [Nontrivial α] (a : α), {a} ≠ Set.univ- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nontrivial
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.
- Setstatement · cited by 53,352
- Set.univstatement and proof · cited by 3,945
- Nontrivialstatement and proof · cited by 2,416
- Eq.supersetproof · cited by 16
- Set.Nontrivial.not_subset_singletonproof · cited by 5
- Set.nontrivial_univproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.isSimpleOrder_blockMem_iff_isPreprimitiveproof · cited by 1
- Set.singleton_ssubset_univproof · cited by 0