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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply set_ext with proj0 (setsum x0 x1), x0 leaving 2 subgoals.
Let x2 of type ι be given.
Assume H0: x2proj0 (setsum x0 x1).
Apply pairE0 with x0, x1, x2.
Apply proj0E with setsum x0 x1, x2.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Assume H0: x2x0.
Apply proj0I with setsum x0 x1, x2.
Apply pairI0 with x0, x1, x2.
The subproof is completed by applying H0.