Theorems · Theorem · convex and discrete geometry

List.sbtw_cons

∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
  [inst_3 : Module R V] [inst_4 : AddTorsor V P] [IsOrderedRing R] {p : P} {l : List P},
  List.Sbtw R (p :: l) ↔ List.Pairwise (Sbtw R p) l ∧ List.Sbtw R l ∧ l ≠ [p]

Defined in

Mathlib.Analysis.Convex.BetweenList

Cited by

0 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleAddTorsorIsOrderedRing