Theorems · Definition · convex and discrete geometry
segment
(𝕜 : Type u_1) → {E : Type u_2} → [Semiring 𝕜] → [PartialOrder 𝕜] → [AddCommMonoid E] → [SMul 𝕜 E] → E → E → Set ESegments in a vector space. Denoted as [x -[𝕜] y] within the Convex namespace.
- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 120 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 119 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Set.ofPredproof · cited by 6,101
Cited by121
Results whose statement or proof uses this declaration.
- convexJoinproof · cited by 31
- Convex.segment_subsetstatement · cited by 22
- segment_eq_image_lineMapstatement and proof · cited by 11
- segment_eq_Iccstatement · cited by 9
- segment_symmstatement and proof · cited by 9
- openSegment_subset_segmentstatement and proof · cited by 8
- left_mem_segmentstatement · cited by 8
- segment_eq_imagestatement and proof · cited by 7
- right_mem_segmentstatement · cited by 7
- convexJoin_commproof · cited by 6
- convex_iff_segment_subsetstatement · cited by 6
- hasStrictFDerivAt_uncurry_coprodproof · cited by 5