Let x0 of type ι be given.
Apply add_SNo_com with
x0,
0,
λ x1 x2 . x2 = x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
Apply add_SNo_0L with
x0.
The subproof is completed by applying H0.