Theorems · Theorem · convex and discrete geometry
StarConvex.neg
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] {x : E} {s : Set E}, StarConvex 𝕜 x s → StarConvex 𝕜 (-x) (-s)- 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.
Cites10
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Set.negstatement · cited by 168
- StarConvexstatement and proof · cited by 62
- Set.image_neg_eq_negproof · cited by 52
- IsLinearMap.isLinearMap_negproof · cited by 3
- StarConvex.is_linear_imageproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- StarConvex.subproof · cited by 0