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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 0.
Assume H3: SNoLt x1 0.
Apply SNoLtLe_or with x0, 0, SNoLe 0 (mul_SNo x0 x1) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
Assume H4: SNoLt x0 0.
Apply SNoLtLe with 0, mul_SNo x0 x1.
Apply mul_SNo_neg_neg with x0, x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
Assume H4: SNoLe 0 x0.
Apply SNoLe_antisym with x0, 0, λ x2 x3 . SNoLe 0 (mul_SNo x3 x1) leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply mul_SNo_zeroL with x1, λ x2 x3 . SNoLe 0 x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying SNoLe_ref with 0.