Theorems · Theorem · convex and discrete geometry

wbtw_lineMap_iff

∀ {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] [IsDomain R] [Module.IsTorsionFree R V] {x y : P}
  {r : R}, Wbtw R x ((AffineMap.lineMap x y) r) y ↔ x = y ∨ r ∈ Set.Icc 0 1

Defined in

Mathlib.Analysis.Convex.Between

Cited by

2 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleAddTorsorIsOrderedRingIsDomainModule.IsTorsionFree