Theorems · Theorem · convex and discrete geometry
StarConvex.openSegment_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 → openSegment 𝕜 x y ⊆ s- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- LE.le.transproof · cited by 3,151
- openSegmentstatement · cited by 102
- StarConvexstatement and proof · cited by 62
- openSegment_subset_segmentproof · cited by 8
- StarConvex.segment_subsetproof · cited by 4
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