Theorems · Theorem · logic and foundations
Set.Nonempty.of_subtype
∀ {α : Type u} {s : Set α} [Nonempty ↑s], s.Nonempty- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Elemstatement and proof · cited by 7,166
- Set.Nonemptystatement · cited by 2,627
- nonempty_subtypeproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- IsIrreducible.of_subtypeproof · cited by 1
- Set.eq_of_nonempty_of_subsingletonproof · cited by 1
- ENat.sSup_mem_of_nonempty_of_lt_topproof · cited by 1
- zero_mem_absConvexHullproof · cited by 0
- IsPGroup.nonempty_fixed_point_of_prime_not_dvd_cardproof · cited by 0