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Proofgold Proof

pf
Claim L0: u23 = add_nat u1 u22
Apply unknownprop_566d903739470afda40d64020ac73735d543ec3209342e2b92a42fa9f217751d with λ x0 : ι → ι . x0, 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 (x0 x1))))))))))))))))))))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_9492eda3f4288329c7343262dda5eae37e08c34cd783f7bb0ddb22a0cc0d8c73.
The subproof is completed by applying unknownprop_cd2e82ef4221082a96ca4495b573c10f870eabc28fd174aa5eb72ee3150cae4b.
Apply L0 with λ x0 x1 . u1ordsucc x1.
Apply unknownprop_65854e80dcdfdaad216d9278c1826bfa6e412eacf7818f3d49e43d93a23f7bcf with u1, u22.
The subproof is completed by applying unknownprop_c873eeccdf6e645ee19271ea61e3647072d01ff54e75e19478129f6b14f6a5a5.