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