Let x0 of type ι be given.
Apply SNo_SNo with
ordsucc (SNoLev x0),
SNo_extend0 x0 leaving 2 subgoals.
Apply ordinal_ordsucc with
SNoLev x0.
Apply SNoLev_ordinal with
x0.
The subproof is completed by applying H0.
Apply SNo_extend0_SNo_ with
x0.
The subproof is completed by applying H0.