∀ {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] {n : ℕ}
  [inst_6 : NeZero n] (s : Affine.Simplex R P n) {w₁ w₂ : Fin (n + 1) → R},
  ∑ j, w₁ j = 1 →
    ∑ j, w₂ j = 1 →
      ∀ {i : Fin (n + 1)},
        0 < w₁ i →
          w₂ i < 0 →
            (affineSpan R (Set.range (s.faceOpposite i).points)).SOppSide
              ((Finset.affineCombination R Finset.univ s.points) w₁)
              ((Finset.affineCombination R Finset.univ s.points) w₂)