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Proofgold Proof

pf
Apply add_nat_add_SNo with 1, 1, λ x0 x1 . x0 = 2 leaving 3 subgoals.
Apply nat_p_omega with 1.
The subproof is completed by applying nat_1.
Apply nat_p_omega with 1.
The subproof is completed by applying nat_1.
The subproof is completed by applying add_nat_1_1_2.