Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
4,
λ x4 . If_i (x4 = 0) x0 (If_i (x4 = 1) x1 (If_i (x4 = 2) x2 x3)),
0,
λ x4 x5 . x5 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_f34554c557ab10b2e58b26abe13035311eb2c5b143ae8ebc22de21fb71a532e5.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
0 = 0,
x0,
If_i (0 = 1) x1 (If_i (0 = 2) x2 x3).
Let x4 of type ι → ι → ο be given.
Assume H0: x4 0 0.
The subproof is completed by applying H0.