Let x0 of type ι be given.
Assume H0: x0 ∈ 2.
Let x1 of type ι → ο be given.
Assume H1: x1 0.
Assume H2: x1 1.
Apply ordsuccE with
1,
x0,
x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H3: x0 ∈ 1.
Apply cases_1 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H1.
Assume H3: x0 = 1.
Apply H3 with
λ x2 x3 . x1 x3.
The subproof is completed by applying H2.