∀ {R : Type u_1} [inst : CommRing R] {c₁ c₂ : R} (a₁ a₂ a₃ a₄ : R),
  CliffordAlgebraQuaternion.ofQuaternion { re := a₁, imI := a₂, imJ := a₃, imK := a₄ } =
    (algebraMap R (CliffordAlgebra (CliffordAlgebraQuaternion.Q c₁ c₂))) a₁ +
          a₂ • (CliffordAlgebra.ι (CliffordAlgebraQuaternion.Q c₁ c₂)) (1, 0) +
        a₃ • (CliffordAlgebra.ι (CliffordAlgebraQuaternion.Q c₁ c₂)) (0, 1) +
      a₄ •
        ((CliffordAlgebra.ι (CliffordAlgebraQuaternion.Q c₁ c₂)) (1, 0) *
          (CliffordAlgebra.ι (CliffordAlgebraQuaternion.Q c₁ c₂)) (0, 1))