Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Assume H0:
∀ x2 . x1 x2 ⟶ ∀ x3 . x3 ∈ x2 ⟶ nIn x0 x3.
Let x2 of type ι be given.
Apply Repl_Empty with
λ x3 . (λ x4 . SetAdjoin x4 x0) x3,
λ x3 x4 . binunion x2 x4 = x2.
The subproof is completed by applying binunion_idr with x2.