Theorems · Theorem · order theory
Set.eq_singleton_iff_nonempty_unique_mem
∀ {α : Type u_1} {s : Set α} {a : α}, s = {a} ↔ s.Nonempty ∧ ∀ x ∈ s, x = a- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, 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.Nonemptystatement and proof · cited by 2,627
- Set.eq_singleton_iff_unique_memproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanGeometry.inter_eq_singleton_orthogonalProjectionproof · cited by 2
- dense_compl_singleton_iff_not_openproof · cited by 1
- IsLocalRing.primesOver_eqproof · cited by 1
- eq_singleton_bot_of_sSup_eq_bot_of_nonemptyproof · cited by 1
- eq_singleton_top_of_sInf_eq_top_of_nonemptyproof · cited by 0