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))))))),
7,
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_24f9b2504e55a53481478efa0004fce723ae17bde3a78496dd945af2a74b32aa.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 0,
x0,
If_i (7 = 1) x1 (If_i (7 = 2) x2 (If_i (7 = 3) x3 (If_i (7 = 4) x4 (If_i (7 = 5) x5 (If_i (7 = 6) x6 (If_i (7 = 7) x7 x8)))))),
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_044b89e987d3823a303739c4fd81b4eb8781fd58daca9dd486dda616a5ef80c4.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 1,
x1,
If_i (7 = 2) x2 (If_i (7 = 3) x3 (If_i (7 = 4) x4 (If_i (7 = 5) x5 (If_i (7 = 6) x6 (If_i (7 = 7) x7 x8))))),
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_90c26469f359ed2ad5519a259f08881a687ca6b2c46838f8f156f0df356f506d.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 2,
x2,
If_i (7 = 3) x3 (If_i (7 = 4) x4 (If_i (7 = 5) x5 (If_i (7 = 6) x6 (If_i (7 = 7) x7 x8)))),
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_3066260e93ea6acec7a7721534624a7e48c3b1fd278a89ec849f8157a4d324f3.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 3,
x3,
If_i (7 = 4) x4 (If_i (7 = 5) x5 (If_i (7 = 6) x6 (If_i (7 = 7) x7 x8))),
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_42616927938edd3fbf02f33283ebbf99811d289fdd8ace98dab3e3ca6e5b7630.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 4,
x4,
If_i (7 = 5) x5 (If_i (7 = 6) x6 (If_i (7 = 7) x7 x8)),
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_70f33f7effe84bb94ffb6d0fd16305fd3ca0f1c4530e1ef7c13d0efed035e353.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 5,
x5,
If_i (7 = 6) x6 (If_i (7 = 7) x7 x8),
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_a48f76420af0c32c22f9c2305712e41cd3d7ef58964b0c2579e9654e172db4df.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
7 = 6,
x6,
If_i (7 = 7) x7 x8,
λ x9 x10 . x10 = x7 leaving 2 subgoals.
The subproof is completed by applying unknownprop_f1cd194676125d8079d7d2963f96231b7375862f18efaf3e71c3451b2ac2e902.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
7 = 7,
x7,
x8.
Let x9 of type ι → ι → ο be given.
Assume H0: x9 7 7.
The subproof is completed by applying H0.