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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: SNoLt 0 x2.
Assume H4: SNoLt x0 x1.
Apply mul_SNo_com with x0, x2, λ x3 x4 . SNoLt x4 (mul_SNo x1 x2) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply mul_SNo_com with x1, x2, λ x3 x4 . SNoLt (mul_SNo x2 x0) x4 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply pos_mul_SNo_Lt with x2, x0, x1 leaving 5 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.