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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Let x2 of type ο be given.
Assume H2: SNoLt x0 x1x2.
Assume H3: x0 = x1x2.
Assume H4: SNoLt x1 x0x2.
Apply SNoLt_trichotomy_or with x0, x1, x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H5: or (SNoLt x0 x1) (x0 = x1).
Apply H5 with x2 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.