Theorems · Theorem · convex and discrete geometry
starConvex_iff_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
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 120
- StarConvexstatement and proof · cited by 62
Cited by3
Results whose statement or proof uses this declaration.
- convex_iff_segment_subsetproof · cited by 6
- StarConvex.segment_subsetproof · cited by 4
- starConvex_iff_openSegment_subsetproof · cited by 1