Theorems · Theorem · convex and discrete geometry

sbtw_iff_left_ne_and_right_mem_image_Ioi

∀ {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},
  Sbtw R x y z ↔ x ≠ y ∧ z ∈ ⇑(AffineMap.lineMap x y) '' Set.Ioi 1

Defined in

Mathlib.Analysis.Convex.Between

Cited by

2 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor