Theorems · Theorem · convex and discrete geometry
StarConvex.smul_mem
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [AddRightMono 𝕜] [inst_3 : AddCommGroup E]
[inst_4 : Module 𝕜 E] {x : E} {s : Set E}, StarConvex 𝕜 0 s → x ∈ s → ∀ {t : 𝕜}, 0 ≤ t → t ≤ 1 → t • x ∈ s- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- zero_addproof · cited by 2,366
- AddRightMonostatement and proof · cited by 367
- StarConvexstatement and proof · cited by 62
- StarConvex.add_smul_memproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- convexHull_sphere_eq_closedBallproof · cited by 1
- StarConvex.mem_smulproof · cited by 0