Proofgold Proof

pf
Let x0 of type ι be given. Assume H0: x0 ∈ quaternion. Apply HSNo_pair_0 with x0, λ x1 x2 . OSNo_proj1 x1 = 0. Apply octonion_p1_eq with x0, 0 leaving 2 subgoals. The subproof is completed by applying H0. The subproof is completed by applying quaternion_0. ■