Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoS_I with
SNoLev x1,
x0,
SNoLev x0 leaving 3 subgoals.
Apply SNoLev_ordinal with
x1.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply SNoLev_ with
x0.
The subproof is completed by applying H0.