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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0 ∈ SNoS_ omega.
Apply SNoS_E2 with omega, x0, diadic_rational_p x0 leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
The subproof is completed by applying H0.
Assume H1: SNoLev x0 ∈ omega.
Assume H2: ordinal (SNoLev x0).
Assume H3: SNo x0.
Assume H4: SNo_ (SNoLev x0) x0.
Apply SNoS_omega_diadic_rational_p_lem with SNoLev x0, x0 leaving 3 subgoals.
Apply omega_nat_p with SNoLev x0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
set y1 to be SNoLev x0
Let x2 of type ι → ι → ο be given.
Assume H5: x2 y1 y1.
The subproof is completed by applying H5.
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