Let x0 of type ι be given.
Let x1 of type ι be given.
Apply HSNo_proj0proj1_split with
x0,
x1 leaving 2 subgoals.
Apply quaternion_HSNo with
x0.
The subproof is completed by applying H0.
Apply quaternion_HSNo with
x1.
The subproof is completed by applying H1.