Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
3,
λ x3 . If_i (x3 = 0) x0 (If_i (x3 = 1) x1 x2),
0,
λ x3 x4 . x4 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_a5b7bb93b9d74b67d23f287359a5c7eb260739fedbe9ea58c164730f644f0cf9.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
0 = 0,
x0,
If_i (0 = 1) x1 x2.
Let x3 of type ι → ι → ο be given.
Assume H0: x3 0 0.
The subproof is completed by applying H0.