∀ {R : Type r} [inst : CommRing R] (W' : WeierstrassCurve.Projective R),
  W'.polynomial =
    MvPolynomial.X 1 ^ 2 * MvPolynomial.X 2 +
          MvPolynomial.C W'.a₁ * MvPolynomial.X 0 * MvPolynomial.X 1 * MvPolynomial.X 2 +
        MvPolynomial.C W'.a₃ * MvPolynomial.X 1 * MvPolynomial.X 2 ^ 2 -
      (MvPolynomial.X 0 ^ 3 + MvPolynomial.C W'.a₂ * MvPolynomial.X 0 ^ 2 * MvPolynomial.X 2 +
          MvPolynomial.C W'.a₄ * MvPolynomial.X 0 * MvPolynomial.X 2 ^ 2 +
        MvPolynomial.C W'.a₆ * MvPolynomial.X 2 ^ 3)