Theorems · Theorem · convex and discrete geometry
StarConvex.segment_subset
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : SMul 𝕜 E] {x : E} {s : Set E}, StarConvex 𝕜 x s → ∀ {y : E}, y ∈ s → segment 𝕜 x y ⊆ s- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- segmentstatement · cited by 120
- StarConvexstatement and proof · cited by 62
- starConvex_iff_segment_subsetproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticConeproof · cited by 1
- StarConvex.isPathConnectedproof · cited by 1
- StarConvex.add_smul_sub_memproof · cited by 0
- StarConvex.openSegment_subsetproof · cited by 0