∀ {V : Type u_2} {P : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {t : Affine.Triangle ℝ P} {i₃ : Fin 3} {p : P} (i : Fin (2 + 1)),
  dist p ↑((Affine.Simplex.faceOpposite t i₃).orthogonalProjectionSpan p) =
      dist p ↑((Affine.Simplex.faceOpposite t i).orthogonalProjectionSpan p) →
    dist p ↑((Affine.Simplex.faceOpposite t i).orthogonalProjectionSpan p) =
      dist p ↑((Affine.Simplex.faceOpposite t i₃).orthogonalProjectionSpan p)