Let x0 of type ι be given.
Apply SNoS_I with
omega,
x0,
x0 leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
The subproof is completed by applying H0.
Apply ordinal_SNoLev with
x0,
λ x1 x2 . SNo_ x1 x0 leaving 2 subgoals.
Apply nat_p_ordinal with
x0.
Apply omega_nat_p with
x0.
The subproof is completed by applying H0.
Apply SNoLev_ with
x0.
Apply omega_SNo with
x0.
The subproof is completed by applying H0.