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Proofgold Proof

pf
Claim L0: u23 = add_nat u21 u2
Apply unknownprop_566d903739470afda40d64020ac73735d543ec3209342e2b92a42fa9f217751d with λ x0 : ι → ι . λ x1 . x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 x1)))))))))))))))))))), λ x0 : ι → ι . λ x1 . x0 (x0 x1) leaving 2 subgoals.
The subproof is completed by applying unknownprop_5736f28d08664b9b7be676af8fe97d8bc5ccb918218c45c8c1dc935bd28d649e.
The subproof is completed by applying unknownprop_97e3ff168096656c305ade85600b40fd44b9a25b42a0301a15eb0995f9b07a20.
Apply L0 with λ x0 x1 . u21ordsucc x1.
Apply unknownprop_65854e80dcdfdaad216d9278c1826bfa6e412eacf7818f3d49e43d93a23f7bcf with u21, u2.
The subproof is completed by applying nat_2.