Let x0 of type ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply xm with
x0,
or (If_i x0 x1 x2 = x1) (If_i x0 x1 x2 = x2) leaving 2 subgoals.
Assume H0: x0.
Apply orIL with
If_i x0 x1 x2 = x1,
If_i x0 x1 x2 = x2.
Apply If_i_1 with
x0,
x1,
x2.
The subproof is completed by applying H0.
Apply orIR with
If_i x0 x1 x2 = x1,
If_i x0 x1 x2 = x2.
Apply If_i_0 with
x0,
x1,
x2.
The subproof is completed by applying H0.