∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Affine F} [inst_1 : DecidableEq F] {x₁ x₂ y₁ y₂ : F}
  {h₁ : W.Nonsingular x₁ y₁} {h₂ : W.Nonsingular x₂ y₂} (hy : y₁ ≠ W.negY x₂ y₂),
  WeierstrassCurve.Affine.Point.some x₁ y₁ h₁ + WeierstrassCurve.Affine.Point.some x₂ y₂ h₂ =
    WeierstrassCurve.Affine.Point.some (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂)) (W.addY x₁ x₂ y₁ (W.slope x₁ x₂ y₁ y₂)) ⋯