Theorems · Theorem · geometry

AffineSubspace.setOfPred_sOppSide_eq_image2

∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P]
  {s : AffineSubspace R P} {x p : P},
  x ∉ s → p ∈ s → {y | s.SOppSide x y} = Set.image2 (fun t q => t • (x -ᵥ p) +ᵥ q) (Set.Iio 0) ↑s

Defined in

Mathlib.Analysis.Convex.Side

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor