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))))))),
4,
λ x9 x10 . x10 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_a64620657818a35f4c967be85c16002e9710d5e0e63acc13f5cd7b89302c4fe4.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 0,
x0,
If_i (4 = 1) x1 (If_i (4 = 2) x2 (If_i (4 = 3) x3 (If_i (4 = 4) x4 (If_i (4 = 5) x5 (If_i (4 = 6) x6 (If_i (4 = 7) x7 x8)))))),
λ x9 x10 . x10 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_eaa778def292ef273cdc44e35415a8a42535318d4e19c13ee6ceed0c5eb3f775.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 1,
x1,
If_i (4 = 2) x2 (If_i (4 = 3) x3 (If_i (4 = 4) x4 (If_i (4 = 5) x5 (If_i (4 = 6) x6 (If_i (4 = 7) x7 x8))))),
λ x9 x10 . x10 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_75032dcd8ad59e83bbbd268576bb90fef789394372056ddc79da134e39e13bc4.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 2,
x2,
If_i (4 = 3) x3 (If_i (4 = 4) x4 (If_i (4 = 5) x5 (If_i (4 = 6) x6 (If_i (4 = 7) x7 x8)))),
λ x9 x10 . x10 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_6e85348d9b8c1714b2cb6d272e0e84b0638dd511839ada963d83f563a6d15dde.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 3,
x3,
If_i (4 = 4) x4 (If_i (4 = 5) x5 (If_i (4 = 6) x6 (If_i (4 = 7) x7 x8))),
λ x9 x10 . x10 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_6959d9e660b21c56708e454ccc9acedd4faf4caf2ab54adc55f634a87d3efc20.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
4 = 4,
x4,
If_i (4 = 5) x5 (If_i (4 = 6) x6 (If_i (4 = 7) x7 x8)).
Let x9 of type ι → ι → ο be given.
Assume H0: x9 4 4.
The subproof is completed by applying H0.