Let x0 of type ο be given.
Let x1 of type ι be given.
Apply xm with
x0,
If_i x0 x1 x1 = x1 leaving 2 subgoals.
Assume H0: x0.
Apply If_i_1 with
x0,
x1,
x1.
The subproof is completed by applying H0.
Apply If_i_0 with
x0,
x1,
x1.
The subproof is completed by applying H0.