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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply pair_ap_0 with x0, x1, λ x2 x3 . setsum x3 (ap (setsum x0 x1) 1) = setsum x0 x1.
Apply pair_ap_1 with x0, x1, λ x2 x3 . setsum x0 x3 = setsum x0 x1.
Let x2 of type ιιο be given.
Assume H0: x2 (setsum x0 x1) (setsum x0 x1).
The subproof is completed by applying H0.