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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0omega.
Let x1 of type ι be given.
Assume H1: x1omega.
Apply mul_nat_mul_SNo with x0, x1, λ x2 x3 . x2omega leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply nat_p_omega with mul_nat x0 x1.
Apply mul_nat_p with x0, x1 leaving 2 subgoals.
Apply omega_nat_p with x0.
The subproof is completed by applying H0.
Apply omega_nat_p with x1.
The subproof is completed by applying H1.