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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: prim1 (aae7a.. (4ae4a.. 4a7ef..) x2) (aae7a.. x0 x1).
Apply unknownprop_583e189228469f510dae093aa816b0d084f1acaf0341e7deab9d9a676d1b11ef with x0, x1, aae7a.. (4ae4a.. 4a7ef..) x2, prim1 x2 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_669df0da86db4f986bae532f93288cb46feb5b77310c7f6de7766507585de4c6 with λ x3 x4 : ι → ι . (∃ x5 . and (prim1 x5 x0) (aae7a.. (4ae4a.. 4a7ef..) x2 = x3 x5))prim1 x2 x1.
Apply unknownprop_48f8d4859b6b78ba3bbfab79f28064a8eb2fee8b3008bbf7332b70f58b78e189 with λ x3 x4 : ι → ι . (∃ x5 . and (prim1 x5 x0) (x3 x2 = f6917.. x5))prim1 x2 x1.
Assume H1: ∃ x3 . and (prim1 x3 x0) (09364.. x2 = f6917.. x3).
Apply FalseE with prim1 x2 x1.
Apply exandE_i with λ x3 . prim1 x3 x0, λ x3 . 09364.. x2 = f6917.. x3, False leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Assume H2: prim1 x3 x0.
Assume H3: 09364.. x2 = f6917.. x3.
Apply unknownprop_eb2fcd306f6f841b66fd8e32d0e8a446cfe3594d26b0bbf0192de86d9ef1a8f4 with x3, x2.
Let x4 of type ιιο be given.
The subproof is completed by applying H3 with λ x5 x6 . x4 x6 x5.
Apply unknownprop_48f8d4859b6b78ba3bbfab79f28064a8eb2fee8b3008bbf7332b70f58b78e189 with λ x3 x4 : ι → ι . (∃ x5 . and (prim1 x5 x1) (x3 x2 = x3 x5))prim1 x2 x1.
Assume H1: ∃ x3 . and (prim1 x3 x1) (09364.. x2 = 09364.. x3).
Apply exandE_i with λ x3 . prim1 x3 x1, λ x3 . 09364.. x2 = 09364.. x3, prim1 x2 x1 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Assume H2: prim1 x3 x1.
Assume H3: 09364.. x2 = 09364.. x3.
Apply unknownprop_47e41120ef0e6cbc7dee61e4e0adec283cb1cf9d56967690cc69f7192955cae0 with x2, x3, λ x4 x5 . prim1 x5 x1 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.