Theorems · Theorem · convex and discrete geometry
segment_eq_image
∀ (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 y : E), segment 𝕜 x y = (fun θ => (1 - θ) • x + θ • y) '' Set.Icc 0 1- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Set.imagestatement and proof · cited by 5,609
- Set.extproof · cited by 2,266
- Set.Iccstatement and proof · cited by 1,702
- AddRightMonostatement and proof · cited by 367
- sub_add_cancelproof · cited by 344
- add_sub_cancel_rightproof · cited by 187
- sub_nonnegproof · cited by 167
Cited by7
Results whose statement or proof uses this declaration.
- segment_eq_image_lineMapproof · cited by 11
- segment_eq_image'proof · cited by 3
- parallelepiped_eq_sum_segmentproof · cited by 2
- segment_subset_closure_openSegmentproof · cited by 2
- segment_inter_subset_endpoint_of_linearIndependent_subproof · cited by 1
- Path.range_subpathAuxproof · cited by 1
- closure_openSegmentproof · cited by 0