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))))))),
8,
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_20ea7932f599290c904a0c67626ee2403cb5b9e559bc4659b86e8470d2fff292.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 0,
x0,
If_i (8 = 1) x1 (If_i (8 = 2) x2 (If_i (8 = 3) x3 (If_i (8 = 4) x4 (If_i (8 = 5) x5 (If_i (8 = 6) x6 (If_i (8 = 7) x7 x8)))))),
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_38badafe683b8286c543490687681ede798b8f87bdad5d80b1d1efdf9a26680d.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 1,
x1,
If_i (8 = 2) x2 (If_i (8 = 3) x3 (If_i (8 = 4) x4 (If_i (8 = 5) x5 (If_i (8 = 6) x6 (If_i (8 = 7) x7 x8))))),
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_01240f1dab11c6195e127a898c50f7971579bc68ee42b2e714b23da144ff53bb.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 2,
x2,
If_i (8 = 3) x3 (If_i (8 = 4) x4 (If_i (8 = 5) x5 (If_i (8 = 6) x6 (If_i (8 = 7) x7 x8)))),
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_d1302ecd2886f91fef321c45183e747aec69bc6414946f02b3570dd7c1546be9.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 3,
x3,
If_i (8 = 4) x4 (If_i (8 = 5) x5 (If_i (8 = 6) x6 (If_i (8 = 7) x7 x8))),
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_3e7a0ace0a32011f90a95928d53aabb566c59d8406c7ed7228e6148f6eff44cd.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 4,
x4,
If_i (8 = 5) x5 (If_i (8 = 6) x6 (If_i (8 = 7) x7 x8)),
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_d0f9f48f32300f7ffd6c96fa02ca8095115c606a8c59e6cd9da614c348abb00c.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 5,
x5,
If_i (8 = 6) x6 (If_i (8 = 7) x7 x8),
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_607a5b4dceb9d3c423506ffeda17e4184da3126f68a960bfc1f8fb8a789e8fff.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 6,
x6,
If_i (8 = 7) x7 x8,
λ x9 x10 . x10 = x8 leaving 2 subgoals.
The subproof is completed by applying unknownprop_3abf32d65fe5f16df6cc27f6256c5c153506efc1107ba42d1d3966c2238ec502.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
8 = 7,
x7,
x8.
The subproof is completed by applying unknownprop_8efd08ebfeb898c6f95d82a7e9ae9d7fb3194362ede7154e2c3a6cec69cf70f9.