Let x0 of type ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply If_i_correct with
x0,
x1,
x2,
If_i x0 x1 x2 = x2 leaving 2 subgoals.
Assume H1:
and x0 (If_i x0 x1 x2 = x1).
Apply H0 with
If_i x0 x1 x2 = x2.
Apply andEL with
x0,
If_i x0 x1 x2 = x1.
The subproof is completed by applying H1.
Apply andER with
not x0,
If_i x0 x1 x2 = x2.
The subproof is completed by applying H1.