Let x0 of type ι be given.
Let x1 of type ι be given.
The subproof is completed by applying Inj1I1 with x1.
Apply H0 with
λ x2 x3 . 0 ∈ x3.
The subproof is completed by applying L1.
Apply Inj0E with
x0,
0,
False leaving 2 subgoals.
The subproof is completed by applying L2.
Let x2 of type ι be given.
Assume H3:
and (x2 ∈ x0) (0 = Inj1 x2).
Apply Inj1NE1 with
x2.
Let x3 of type ι → ι → ο be given.
Apply andER with
x2 ∈ x0,
0 = Inj1 x2,
λ x4 x5 . x3 x5 x4.
The subproof is completed by applying H3.