Let x0 of type ι be given.
Assume H0: x0 ∈ 3.
Let x1 of type ι → ο be given.
Assume H1: x1 0.
Assume H2: x1 1.
Assume H3: x1 2.
Apply ordsuccE with
2,
x0,
x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H4: x0 ∈ 2.
Apply cases_2 with
x0,
x1 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H4: x0 = 2.
Apply H4 with
λ x2 x3 . x1 x3.
The subproof is completed by applying H3.