Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply beta with
3,
λ x3 . If_i (x3 = 0) x0 (If_i (x3 = 1) x1 x2),
2,
λ x3 x4 . x4 = x2 leaving 2 subgoals.
The subproof is completed by applying In_2_3.
Apply If_i_0 with
2 = 0,
x0,
If_i (2 = 1) x1 x2,
λ x3 x4 . x4 = x2 leaving 2 subgoals.
The subproof is completed by applying neq_2_0.
Apply If_i_0 with
2 = 1,
x1,
x2.
The subproof is completed by applying neq_2_1.