Theorems · Theorem · logic and foundations
Set.nonempty_of_encard_ne_zero
∀ {α : Type u_1} {s : Set α}, s.encard ≠ 0 → s.Nonempty- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 53,352
- ENatstatement · cited by 4,985
- Set.Nonemptystatement · cited by 2,627
- Set.encardstatement and proof · cited by 327
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Set.encard_eq_zeroproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Set.encard_eq_oneproof · cited by 6
- Set.encard_eq_threeproof · cited by 2
- Set.encard_eq_twoproof · cited by 2
- Set.encard_eq_fourproof · cited by 1
- Set.encard_eq_add_one_iffproof · cited by 0