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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 1.
Assume H3: SNoLe 0 x1.
Apply mul_SNo_oneL with x1, λ x2 x3 . SNoLe (mul_SNo x0 x1) x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply nonneg_mul_SNo_Le' with x0, 1, x1 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_1.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H2.
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