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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: nat_p x0.
Assume H1: ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . SNo x5 ⟶ SNoLev x5 = x4 ⟶ diadic_rational_p x5.
Assume H2: SNo x1.
Assume H3: SNoLev x1 = x0.
Assume H4: not (diadic_rational_p x1).
Assume H5: SNo_max_of (SNoL x1) x2.
Assume H6: SNo x2.
Assume H7: SNoLev x2 ∈ SNoLev x1.
Assume H8: SNoLt x2 x1.
Assume H9: SNo_min_of (SNoR x1) x3.
Assume H10: SNoLev x3 ∈ SNoLev x1.
Assume H11: SNoLt x1 x3.
Assume H12: SNo (add_SNo x1 x1).
Assume H13: SNo (add_SNo x2 x3).
Assume H14: diadic_rational_p x2.
Assume H15: diadic_rational_p x3.
Apply H4.
Apply SNoS_omega_diadic_rational_p_lem with x0, x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
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