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.
Let x4 of type ι be given.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
5,
λ x5 . If_i (x5 = 0) x0 (If_i (x5 = 1) x1 (If_i (x5 = 2) x2 (If_i (x5 = 3) x3 x4))),
0,
λ x5 x6 . x6 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_86d6d81630b243115c43d8ccb529fedcd7cd5f30707d2dd4a404787d805287ea.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
0 = 0,
x0,
If_i (0 = 1) x1 (If_i (0 = 2) x2 (If_i (0 = 3) x3 x4)).
Let x5 of type ι → ι → ο be given.
Assume H0: x5 0 0.
The subproof is completed by applying H0.