Let x0 of type ι be given.
Apply octonion_I with
minus_HSNo (OSNo_proj0 x0),
minus_HSNo (OSNo_proj1 x0) leaving 2 subgoals.
Apply quaternion_minus_HSNo with
OSNo_proj0 x0.
Apply octonion_p0_quaternion with
x0.
The subproof is completed by applying H0.
Apply quaternion_minus_HSNo with
OSNo_proj1 x0.
Apply octonion_p1_quaternion with
x0.
The subproof is completed by applying H0.