Let x0 of type ι be given.
Assume H0: x0 ∈ 1.
Apply ordsuccE with
0,
x0,
x0 ∈ Sing 0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x0 ∈ 0.
Apply FalseE with
x0 ∈ Sing 0.
Apply EmptyE with
x0.
The subproof is completed by applying H1.
Assume H1: x0 = 0.
Apply H1 with
λ x1 x2 . x2 ∈ Sing 0.
The subproof is completed by applying SingI with 0.