Theorems · Theorem · logic and foundations
Set.not_nonempty_iff_eq_empty
∀ {α : Type u} {s : Set α}, ¬s.Nonempty ↔ s = ∅See also Set.nonempty_iff_ne_empty.
- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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 · cited by 2,627
Cited by56
Results whose statement or proof uses this declaration.
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Metric.ball_eq_emptyproof · cited by 16
- Metric.closedBall_eq_emptyproof · cited by 15
- Set.image2_eq_empty_iffproof · cited by 10
- IsCompact.exists_isLeastproof · cited by 9
- Set.prod_eq_empty_iffproof · cited by 8
- notMem_tsupport_iff_eventuallyEqproof · cited by 7
- Set.preimage_singleton_eq_emptyproof · cited by 5
- Set.singleton_inter_eq_emptyproof · cited by 5
- Set.range_eq_empty_iffproof · cited by 5
- Nat.nonempty_of_pos_sInfproof · cited by 4
- MeasureTheory.ae_eq_topproof · cited by 4