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Proofgold Proof

pf
Claim L0: u23 = add_nat u11 u12
Apply unknownprop_566d903739470afda40d64020ac73735d543ec3209342e2b92a42fa9f217751d with λ x0 : ι → ι . λ x1 . x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 x1)))))))))), λ x0 : ι → ι . λ x1 . x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 (x0 x1))))))))))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_ed572293a6fa0ec02a803cad7d3df6b0e0146a679954f245b5255a74225de76b.
The subproof is completed by applying unknownprop_e8e6d5cd52803fa78978937f5cadf0b90ae1da5571c1821cbca428bd99b61202.
Apply L0 with λ x0 x1 . u11ordsucc x1.
Apply unknownprop_65854e80dcdfdaad216d9278c1826bfa6e412eacf7818f3d49e43d93a23f7bcf with u11, u12.
The subproof is completed by applying nat_12.