Proofgold Proof

pf
Let x0 of type ι be given. Assume H0: x0 ∈ quaternion. Apply HSNo_pair_0 with x0, λ x1 x2 . x1 ∈ octonion. Apply octonion_I with x0, 0 leaving 2 subgoals. The subproof is completed by applying H0. The subproof is completed by applying quaternion_0. ■