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.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
9,
λ x9 . If_i (x9 = 0) x0 (If_i (x9 = 1) x1 (If_i (x9 = 2) x2 (If_i (x9 = 3) x3 (If_i (x9 = 4) x4 (If_i (x9 = 5) x5 (If_i (x9 = 6) x6 (If_i (x9 = 7) x7 x8))))))),
0,
λ x9 x10 . x10 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_49b292b56851f9f5c6ff4b56ce734e62f5bf2699a8110543fe1b44e31aec06c9.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
0 = 0,
x0,
If_i (0 = 1) x1 (If_i (0 = 2) x2 (If_i (0 = 3) x3 (If_i (0 = 4) x4 (If_i (0 = 5) x5 (If_i (0 = 6) x6 (If_i (0 = 7) x7 x8)))))).
Let x9 of type ι → ι → ο be given.
Assume H0: x9 0 0.
The subproof is completed by applying H0.