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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: nat_p x0.
Let x1 of type ι be given.
Assume H1: x1setminus omega 1.
Apply mul_nat_com with x1, x0, λ x2 x3 . x0x3 leaving 3 subgoals.
Apply omega_nat_p with x1.
Apply setminusE1 with omega, 1, x1.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply unknownprop_0dc8d11d1ba28645d1565e6f95fe26f514da291413e114d0327c09556f7d23e9 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.