Theorems · Theorem · logic and foundations
Set.encard_eq_three
∀ {α : Type u_1} {s : Set α}, s.encard = 3 ↔ ∃ x y z, x ≠ y ∧ x ≠ z ∧ y ≠ z ∧ s = {x, y, z}- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- ENatstatement and proof · cited by 4,985
- Set.encardstatement and proof · cited by 327
- Eq.subsetproof · cited by 124
- Set.insert_eq_of_memproof · cited by 118
- Set.insert_sdiff_singletonproof · cited by 28
- Set.encard_singletonproof · cited by 26
- Set.encard_insert_of_notMemproof · cited by 17
- ENat.one_ne_topproof · cited by 15
- ENat.addLECancellable_of_ne_topproof · cited by 9
- AddLECancellable.inj_leftproof · cited by 6
- Set.nonempty_of_encard_ne_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Set.encard_eq_fourproof · cited by 1
- Set.ncard_eq_threeproof · cited by 0