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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.
Let x3 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNoLt 0 x0.
Assume H5: SNoLt 0 x1.
Assume H6: SNoLt x0 x2.
Assume H7: SNoLt x1 x3.
Apply SNoLt_tra with mul_SNo x0 x1, mul_SNo x0 x3, mul_SNo x2 x3 leaving 5 subgoals.
Apply SNo_mul_SNo with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_mul_SNo with x0, x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply SNo_mul_SNo with x2, x3 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply pos_mul_SNo_Lt with x0, x1, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H7.
Apply pos_mul_SNo_Lt' with x0, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply SNoLt_tra with 0, x1, x3 leaving 5 subgoals.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
The subproof is completed by applying H7.
The subproof is completed by applying H6.