Let x0 of type ι be given.
Let x1 of type ι be given.
Apply add_SNo_0R with
x0,
λ x2 x3 . SNoLt x2 (add_SNo x0 (eps_ x1)) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply add_SNo_Lt2 with
x0,
0,
eps_ x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
Apply SNo_eps_ with
x1.
The subproof is completed by applying H1.
Apply SNo_eps_pos with
x1.
The subproof is completed by applying H1.