Let x0 of type ι be given.
Apply ordinal_SNoR with
x0,
λ x1 x2 . SNoCutP (SNoS_ x0) x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply ordinal_SNoL with
x0,
λ x1 x2 . SNoCutP x1 (SNoR x0) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply SNoCutP_SNoL_SNoR with
x0.
Apply ordinal_SNo with
x0.
The subproof is completed by applying H0.