Let x0 of type ι be given.
Assume H0:
x0 ∈ UPair 0 1.
Apply UPairE with
x0,
0,
1,
x0 ∈ 2 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x0 = 0.
Apply H1 with
λ x1 x2 . x2 ∈ 2.
The subproof is completed by applying In_0_2.
Assume H1: x0 = 1.
Apply H1 with
λ x1 x2 . x2 ∈ 2.
The subproof is completed by applying In_1_2.