Theorems · Theorem · convex and discrete geometry

Collinear.wbtw_or_wbtw_or_wbtw

∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R]
  [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P] {x y z : P},
  Collinear R {x, y, z} → Wbtw R x y z ∨ Wbtw R y z x ∨ Wbtw R z x y

Defined in

Mathlib.Analysis.Convex.Between

Cited by

3 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor