Let x0 of type ι be given.
Let x1 of type ι be given.
Apply set_ext with
proj1 (setsum x0 x1),
x1 leaving 2 subgoals.
Let x2 of type ι be given.
Apply pairE1 with
x0,
x1,
x2.
Apply proj1E with
setsum x0 x1,
x2.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Assume H0: x2 ∈ x1.
Apply proj1I with
setsum x0 x1,
x2.
Apply pairI1 with
x0,
x1,
x2.
The subproof is completed by applying H0.