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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_56bd0714abefd533b13603d171a24196c02fb0b6a0af8036287a8ec089f8957d with λ x2 x3 : ι → ο . x3 x0In x0 x1In (ap x0 1) (ap x1 (ap x0 0)).
Assume H0: setsum (ap x0 0) (ap x0 1) = x0.
Assume H1: In x0 x1.
Apply unknownprop_5790343a8368d4f3aa514e68a19a3e4824006be2aed8a0a7a707f542e4c79154 with x1, ap x0 0, ap x0 1.
Apply H0 with λ x2 x3 . In x3 x1.
The subproof is completed by applying H1.