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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Apply xm with SNoLe 0 x0, SNo (abs_SNo x0) leaving 2 subgoals.
Assume H1: SNoLe 0 x0.
Apply nonneg_abs_SNo with x0, λ x1 x2 . SNo x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Assume H1: not (SNoLe 0 x0).
Apply not_nonneg_abs_SNo with x0, λ x1 x2 . SNo x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with x0.
The subproof is completed by applying H0.