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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.
Apply SNo_add_SNo_3c with mul_SNo x2 x1, mul_SNo x0 x3, mul_SNo x2 x3 leaving 3 subgoals.
Apply SNo_mul_SNo with x2, x1 leaving 2 subgoals.
The subproof is completed by applying H2.
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.