Let x0 of type ι be given.
Assume H0: x0 ∈ 2.
Apply ordsuccE with
1,
x0,
x0 ∈ UPair 0 1 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x0 ∈ 1.
Claim L2: x0 = 0
Apply SingE with
0,
x0.
Apply Subq_1_Sing0 with
x0.
The subproof is completed by applying H1.
Apply L2 with
λ x1 x2 . x2 ∈ UPair 0 1.
The subproof is completed by applying UPairI1 with 0, 1.
Assume H1: x0 = 1.
Apply H1 with
λ x1 x2 . x2 ∈ UPair 0 1.
The subproof is completed by applying UPairI2 with 0, 1.