Theorems · Theorem · order theory
Set.Infinite.nonempty
∀ {α : Type u} {s : Set α}, s.Infinite → s.Nonempty- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.Infinitestatement and proof · cited by 263
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Set.finite_emptyproof · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- Pell.exists_of_not_isSquareproof · cited by 3
- SimpleGraph.ComponentCompl.infinite_iff_in_all_rangesproof · cited by 2
- Set.infinite_prodproof · cited by 2
- WellFoundedGT.finite_of_sSupIndepproof · cited by 2
- MvPolynomial.funext_setproof · cited by 2
- exists_topology_isEmbedding_natproof · cited by 1