Theorems · Theorem · logic and foundations
Set.Nonempty.some_mem
∀ {α : Type u} {s : Set α} (h : s.Nonempty), h.some ∈ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.Nonempty.somestatement · cited by 53
Cited by42
Results whose statement or proof uses this declaration.
- AffineSubspace.ext_of_direction_eqproof · cited by 11
- AEMeasurable.exists_ae_eq_range_subsetproof · cited by 4
- Partition.rep_memproof · cited by 3
- 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.ordConnectedProj_mem_ordConnectedComponentproof · cited by 3
- MeasureTheory.ae_bdd_norm_condExp_of_ae_bdd_normproof · cited by 2
- Hindman.exists_FP_of_largeproof · cited by 2
- Hindman.exists_FS_of_largeproof · cited by 2
- PiNat.exists_lipschitz_retraction_of_isClosedproof · cited by 2
- Order.Ideal.bot_memproof · cited by 2