Theorems · Definition · convex and discrete geometry
List.Sbtw
(R : Type u_1) →
{V : Type u_2} →
{P : Type u_4} →
[inst : Ring R] → [PartialOrder R] → [inst_2 : AddCommGroup V] → [Module R V] → [AddTorsor V P] → List P → PropThe points in a list are strictly in that order on a line.
- Defined in
- Mathlib.Analysis.Convex.BetweenList
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Quot.sound
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.
- 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
- AddTorsorstatement and proof · cited by 1,657
- List.Wbtwproof · cited by 15
Cited by14
Results whose statement or proof uses this declaration.
- Function.Injective.list_sbtw_map_iffstatement and proof · cited by 2
- List.SortedLT.sbtwstatement · cited by 1
- List.exists_map_eq_of_sorted_nonempty_iff_sbtwstatement and proof · cited by 1
- List.sbtw_iff_triplewise_and_ne_pairstatement · cited by 1
- List.sbtw_triplestatement · cited by 0
- List.Sbtw.pairwise_nestatement and proof · cited by 0
- List.Sbtw.wbtwstatement and proof · cited by 0
- List.exists_map_eq_of_sorted_iff_sbtwstatement and proof · cited by 0
- AffineEquiv.list_sbtw_map_iffstatement · cited by 0
- List.sbtw_consstatement and proof · cited by 0
- List.sbtw_fourstatement · cited by 0
- List.sbtw_nilstatement · cited by 0