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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.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNoLe x0 x1.
Assume H4: SNoLt x1 x2.
Apply PNoLeLt_tra with SNoLev x0, SNoLev x1, SNoLev x2, λ x3 . x3x0, λ x3 . x3x1, λ x3 . x3x2 leaving 5 subgoals.
Apply SNoLev_ordinal with x0.
The subproof is completed by applying H0.
Apply SNoLev_ordinal with x1.
The subproof is completed by applying H1.
Apply SNoLev_ordinal with x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.