Theorems · Theorem · convex and discrete geometry
convex_singleton
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] (c : E), Convex 𝕜 {c}- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 19 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 · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Convexstatement · cited by 551
- Set.subsingleton_singletonproof · cited by 36
- Set.Subsingleton.convexproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- convexHull_singletonproof · cited by 7
- Convex.vaddproof · cited by 4
- geometric_hahn_banach_open_pointproof · cited by 3
- RCLike.geometric_hahn_banach_closed_pointproof · cited by 3
- Continuous.exists_contMDiff_approx_and_eqOnproof · cited by 2
- geometric_hahn_banach_closed_pointproof · cited by 2
- ProperCone.hyperplane_separation_pointproof · cited by 2
- geometric_hahn_banach_of_nonempty_interior_pointproof · cited by 1
- geometric_hahn_banach_point_pointproof · cited by 1
- RCLike.geometric_hahn_banach_point_closedproof · cited by 1
- convex_zeroproof · cited by 0
- geometric_hahn_banach_point_closedproof · cited by 0