∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {s : AffineSubspace ℝ P} [inst_4 : Nonempty ↥s]
  [inst_5 : s.direction.HasOrthogonalProjection] {p q : P},
  q ∈ s → s.signedInfDist p = (signedDist (p -ᵥ ↑((EuclideanGeometry.orthogonalProjection s) p))) q