Theorems · Theorem · convex and discrete geometry
StarConvex.add
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] {x y : E} {s t : Set E}, StarConvex 𝕜 x s → StarConvex 𝕜 y t → StarConvex 𝕜 (x + y) (s + t)- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- 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
- Set.addstatement · cited by 338
- StarConvexstatement and proof · cited by 62
- Set.add_image_prodproof · cited by 8
- IsLinearMap.isLinearMap_addproof · cited by 3
- StarConvex.is_linear_imageproof · cited by 3
- StarConvex.prodproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- StarConvex.subproof · cited by 0