Let x0 of type ι be given.
Apply SNoS_E2 with
omega,
x0,
SNo x0 leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
Apply diadic_rational_p_SNoS_omega with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H3.