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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: 80242.. x0.
Claim L1: ordinal (e4431.. x0)
Apply unknownprop_afbf697e4489c80654ae2bc4c6605f6f1d2a8b7dcfe3f07863a96592ab5c88f5 with x0.
The subproof is completed by applying H0.
Apply PNoEq_tra_ with e4431.. x0, λ x1 . prim1 x1 (09072.. (4ae4a.. (e4431.. x0)) (λ x2 . or (prim1 x2 x0) (x2 = e4431.. x0))), λ x1 . or (prim1 x1 x0) (x1 = e4431.. x0), λ x1 . prim1 x1 x0 leaving 2 subgoals.
Apply PNoEq_antimon_ with λ x1 . prim1 x1 (09072.. (4ae4a.. (e4431.. x0)) (λ x2 . or (prim1 x2 x0) (x2 = e4431.. x0))), λ x1 . or (prim1 x1 x0) (x1 = e4431.. x0), 4ae4a.. (e4431.. x0), e4431.. x0 leaving 3 subgoals.
Apply unknownprop_1f03c3e4cc230143731a84d6351b78522f6051d5113f644774435abf9cb5a984 with e4431.. x0.
The subproof is completed by applying L1.
The subproof is completed by applying unknownprop_38ce50d6b52a0a920b530e7796207ec902a42d65414467df1ecd3efb123f4cb9 with e4431.. x0.
Apply unknownprop_8ab8782df8e80eb287fd4c918f7b35b584f8954d0de002e6915e8d87848fc5f4 with 4ae4a.. (e4431.. x0), λ x1 . or (prim1 x1 x0) (x1 = e4431.. x0).
Apply unknownprop_1f03c3e4cc230143731a84d6351b78522f6051d5113f644774435abf9cb5a984 with e4431.. x0.
The subproof is completed by applying L1.
Apply PNoEq_sym_ with e4431.. x0, λ x1 . prim1 x1 x0, λ x1 . or (prim1 x1 x0) (x1 = e4431.. x0).
The subproof is completed by applying PNo_extend1_eq with e4431.. x0, λ x1 . prim1 x1 x0.