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.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
7,
λ x7 . If_i (x7 = 0) x0 (If_i (x7 = 1) x1 (If_i (x7 = 2) x2 (If_i (x7 = 3) x3 (If_i (x7 = 4) x4 (If_i (x7 = 5) x5 x6))))),
2,
λ x7 x8 . x8 = x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_9dc257bbcc17b39549f752c5cb424c7b65cdc03a03520837cb1815dd9056a3cd.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
2 = 0,
x0,
If_i (2 = 1) x1 (If_i (2 = 2) x2 (If_i (2 = 3) x3 (If_i (2 = 4) x4 (If_i (2 = 5) x5 x6)))),
λ x7 x8 . x8 = x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_47a023fb65dad0adf6176d6e56f8225fed35ae41cdd7dbd441c63ff764631416.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
2 = 1,
x1,
If_i (2 = 2) x2 (If_i (2 = 3) x3 (If_i (2 = 4) x4 (If_i (2 = 5) x5 x6))),
λ x7 x8 . x8 = x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_6cb9d1d6bff551a32dbdd07e389ec1293336d9b518cb846bc58565f53757a830.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
2 = 2,
x2,
If_i (2 = 3) x3 (If_i (2 = 4) x4 (If_i (2 = 5) x5 x6)).
Let x7 of type ι → ι → ο be given.
Assume H0: x7 2 2.
The subproof is completed by applying H0.