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.
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: x2 ∈ x0.
Apply proj0I with
setsum x0 x1,
x2.
Apply pairI0 with
x0,
x1,
x2.
The subproof is completed by applying H0.