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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 x1 x2.
Apply SNoLeE with x1, x2, SNoLe (add_SNo x0 x1) (add_SNo x0 x2) leaving 5 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Assume H4: SNoLt x1 x2.
Apply SNoLtLe with add_SNo x0 x1, add_SNo x0 x2.
Apply add_SNo_Lt2 with x0, x1, x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Assume H4: x1 = x2.
Apply H4 with λ x3 x4 . SNoLe (add_SNo x0 x4) (add_SNo x0 x2).
The subproof is completed by applying SNoLe_ref with add_SNo x0 x2.
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