Let x0 of type ι be given.
Assume H0: x0 ∈ 1.
Let x1 of type ι → ο be given.
Assume H1: x1 0.
Apply ordsuccE with
0,
x0,
x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H2: x0 ∈ 0.
Apply EmptyE with
x0,
x1 x0.
The subproof is completed by applying H2.
Assume H2: x0 = 0.
Apply H2 with
λ x2 x3 . x1 x3.
The subproof is completed by applying H1.