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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.
Assume H2: SNoLe x0 x1.
Apply SNoLeE with x0, x1, SNoLe (minus_SNo x1) (minus_SNo x0) leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H3: SNoLt x0 x1.
Apply SNoLtLe with minus_SNo x1, minus_SNo x0.
Apply minus_SNo_Lt_contra with x0, x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Assume H3: x0 = x1.
Apply H3 with λ x2 x3 . SNoLe (minus_SNo x1) (minus_SNo x3).
The subproof is completed by applying SNoLe_ref with minus_SNo x1.
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