Let x0 of type ι be given.
Apply SNoLev_prop with
x0,
SNoLev x0 = x0 leaving 2 subgoals.
Apply ordinal_SNo with
x0.
The subproof is completed by applying H0.
Apply SNoLev_uniq with
x0,
SNoLev x0,
x0 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply ordinal_SNo_ with
x0.
The subproof is completed by applying H0.