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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: ordinal x0.
Assume H1: ordinal x1.
Assume H2: x0x1.
Let x2 of type ι be given.
Assume H3: x2SNoS_ x0.
Apply SNoS_E with x0, x2, x2SNoS_ x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Let x3 of type ι be given.
Assume H4: (λ x4 . and (x4x0) (SNo_ x4 x2)) x3.
Apply H4 with x2SNoS_ x1.
Assume H5: x3x0.
Assume H6: SNo_ x3 x2.
Apply SNoS_I with x1, x2, x3 leaving 3 subgoals.
The subproof is completed by applying H1.
Apply H2 with x3.
The subproof is completed by applying H5.
The subproof is completed by applying H6.