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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.
Apply SNoLt_trichotomy_or with x0, x1, or (SNoLt x0 x1) (SNoLe x1 x0) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: or (SNoLt x0 x1) (x0 = x1).
Apply H2 with or (SNoLt x0 x1) (SNoLe x1 x0) leaving 2 subgoals.
Assume H3: SNoLt x0 x1.
Apply orIL with SNoLt x0 x1, SNoLe x1 x0.
The subproof is completed by applying H3.
Assume H3: x0 = x1.
Apply orIR with SNoLt x0 x1, SNoLe x1 x0.
Apply H3 with λ x2 x3 . SNoLe x1 x3.
The subproof is completed by applying SNoLe_ref with x1.
Assume H2: SNoLt x1 x0.
Apply orIR with SNoLt x0 x1, SNoLe x1 x0.
Apply SNoLtLe with x1, x0.
The subproof is completed by applying H2.