Theorems · Definition · logic and foundations
Set.Nonempty.some
{α : Type u} → {s : Set α} → s.Nonempty → αExtract a witness from s.Nonempty. This function might be used instead of case analysis
on the argument. Note that it makes a proof depend on the Classical.choice axiom.
- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses Classical.choice
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 and proof · cited by 2,627
Cited by61
Results whose statement or proof uses this declaration.
- Set.Nonempty.some_memstatement · cited by 42
- AffineSubspace.ext_of_direction_eqproof · cited by 11
- Partition.repproof · cited by 7
- Set.ordConnectedProjproof · cited by 7
- CantorScheme.inducedMapproof · cited by 5
- ShrinkingLemma.PartialRefinement.findproof · cited by 4
- AEMeasurable.exists_ae_eq_range_subsetproof · cited by 4
- Convex.helly_theorem'proof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- CantorScheme.map_memproof · cited by 3
- Set.Nonempty.some.congr_simpstatement and proof · cited by 3
- NormedRing.algEquivComplexOfCompleteproof · cited by 3