Theorems · Theorem · convex and discrete geometry

isVisible_iff_lineMap

∀ {𝕜 : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsOrderedRing 𝕜]
  [inst_3 : AddCommGroup V] [inst_4 : Module 𝕜 V] [inst_5 : AddTorsor V P] {s : Set P} {x y : P},
  x ≠ y → (IsVisible 𝕜 s x y ↔ ∀ δ ∈ Set.Ioo 0 1, (AffineMap.lineMap x y) δ ∉ s)

Defined in

Mathlib.Analysis.Convex.Visible

Cited by

0 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsOrderedRingAddCommGroupModuleAddTorsor