Theorems · Theorem · convex and discrete geometry

AffineIndependent.not_wbtw_of_injective

∀ {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] {ι : Type u_6} (i j k : ι),
  Function.Injective ![i, j, k] → ∀ {T : ι → P}, AffineIndependent R T → ¬Wbtw R (T i) (T j) (T k)

If T is an affine independent family of points, then any 3 distinct points form a triangle.

Defined in

Mathlib.Analysis.Convex.Between

Cited by

0 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor