Theorems · Theorem · order theory
Set.eq_empty_or_singleton_of_subsingleton
∀ {α : Type u} [Subsingleton α] (s : Set α), s = ∅ ∨ ∃ a, s = {a}- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subsingleton
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.Subsingleton.eq_empty_or_singletonproof · cited by 16
- Set.subsingleton_of_subsingletonproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Set.eq_empty_or_singleton_of_uniqueproof · cited by 1
- hasFDerivWithinAt_of_subsingletonproof · cited by 0