Let x0 of type ο be given.
Apply xm with
x0,
If_i x0 1 0 ∈ 2 leaving 2 subgoals.
Assume H0: x0.
Apply If_i_1 with
x0,
1,
0,
λ x1 x2 . x2 ∈ 2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying In_1_2.
Apply If_i_0 with
x0,
1,
0,
λ x1 x2 . x2 ∈ 2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying In_0_2.