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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.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))), λ x8 . If_i (x8 = 4a7ef..) x0 (If_i (x8 = 4ae4a.. 4a7ef..) x1 (If_i (x8 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x8 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x8 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x8 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x8 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))), 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))), λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_17ec03aaff693481db255baef04778877ddc93b6d7801a517ca796f97478580e.
Apply If_i_0 with 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4a7ef.., x0, If_i (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. 4a7ef..) x1 (If_i (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7))))), λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_8901a548ef1b9c69f33a6a5f5df68d5139a5a41ee9e7b9320ae09543356a1125.