Theorems · Theorem · convex and discrete geometry
Convexity.IsConvexSet.of_subsingleton
∀ {R : Type u_3} {X : Type u_5} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R]
[inst_3 : Convexity.ConvexSpace R X] {s : Set X}, s.Subsingleton → Convexity.IsConvexSet R s- Defined in
- Mathlib.Geometry.Convex.Set
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Set.Subsingletonstatement and proof · cited by 276
- Convexity.ConvexSpacestatement and proof · cited by 176
- Convexity.IsConvexSetstatement · cited by 35
- Set.Subsingleton.eq_empty_or_singletonproof · cited by 16
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.