Let x0 of type ι → ι be given.
Apply Empty_Subq_eq with
famunion 0 (λ x1 . x0 x1).
Let x1 of type ι be given.
Assume H0:
x1 ∈ famunion 0 (λ x2 . x0 x2).
Apply famunionE_impred with
0,
x0,
x1,
x1 ∈ 0 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Assume H1: x2 ∈ 0.
Apply FalseE with
x1 ∈ x0 x2 ⟶ x1 ∈ 0.
Apply EmptyE with
x2.
The subproof is completed by applying H1.