{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : Ring A] →
        [inst_2 : Algebra R A] →
          {c₁ c₂ c₃ : R} →
            {motive : QuaternionAlgebra.Basis A c₁ c₂ c₃ → Sort u} →
              (t : QuaternionAlgebra.Basis A c₁ c₂ c₃) →
                ((i j k : A) →
                    (i_mul_i : i * i = c₁ • 1 + c₂ • i) →
                      (j_mul_j : j * j = c₃ • 1) →
                        (i_mul_j : i * j = k) →
                          (j_mul_i : j * i = c₂ • j - k) →
                            motive
                              { i := i, j := j, k := k, i_mul_i := i_mul_i, j_mul_j := j_mul_j, i_mul_j := i_mul_j,
                                j_mul_i := j_mul_i }) →
                  motive t