Theorems · Theorem · convex and discrete geometry

Convex.mapsTo_lineMap

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : Module 𝕜 E] {s : Set E} [AddRightMono 𝕜],
  Convex 𝕜 s → ∀ {x y : E}, x ∈ s → y ∈ s → Set.MapsTo (⇑(AffineMap.lineMap x y)) (Set.Icc 0 1) s

Defined in

Mathlib.Analysis.Convex.Basic

Cited by

3 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleAddRightMono