∀ {𝕜 : Type u_1} {V : Type u_2} {P : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup V]
  [inst_2 : InnerProductSpace 𝕜 V] [inst_3 : MetricSpace P] [inst_4 : NormedAddTorsor V P] {s : AffineSubspace 𝕜 P}
  [inst_5 : Nonempty ↥s] [inst_6 : s.direction.HasOrthogonalProjection],
  (↑(EuclideanGeometry.orthogonalProjection s)).linear = ↑s.direction.orthogonalProjection