(p : Type u_2) →
  (q : Type u_3) →
    (R : Type u₂) →
      [inst : DecidableEq p] →
        [inst_1 : DecidableEq q] →
          [inst_2 : CommRing R] →
            [inst_3 : Fintype p] →
              [inst_4 : Fintype q] →
                {i : R} → i * i = -1 → ↥(LieAlgebra.Orthogonal.so' p q R) ≃ₗ⁅R⁆ ↥(LieAlgebra.Orthogonal.so (p ⊕ q) R)