Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0:
setsum x2 x3 ∈ lam x0 (λ x4 . x1 x4).
Apply proj0_pair_eq with
x2,
x3,
λ x4 x5 . x3 ∈ x1 x4.
Apply proj1_pair_eq with
x2,
x3,
λ x4 x5 . x4 ∈ x1 (proj0 (setsum x2 x3)).
Apply proj1_Sigma with
x0,
x1,
setsum x2 x3.
The subproof is completed by applying H0.