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))))))),
5,
λ x9 x10 . x10 = x5 leaving 2 subgoals.
The subproof is completed by applying unknownprop_fe86c4ed3986bd8840c6664f1e6ddcec6eecccd7b79731fd8e7461f9c8f1edc4.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
5 = 0,
x0,
If_i (5 = 1) x1 (If_i (5 = 2) x2 (If_i (5 = 3) x3 (If_i (5 = 4) x4 (If_i (5 = 5) x5 (If_i (5 = 6) x6 (If_i (5 = 7) x7 x8)))))),
λ x9 x10 . x10 = x5 leaving 2 subgoals.
The subproof is completed by applying unknownprop_e62e52cc6063d20631a5ccc30b538c4ea53badc2fe85f4a4a1692b7ddf2581bd.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
5 = 1,
x1,
If_i (5 = 2) x2 (If_i (5 = 3) x3 (If_i (5 = 4) x4 (If_i (5 = 5) x5 (If_i (5 = 6) x6 (If_i (5 = 7) x7 x8))))),
λ x9 x10 . x10 = x5 leaving 2 subgoals.
The subproof is completed by applying unknownprop_12906250f8e0990d9971cf69beea94e51c503f0bf662b1d8b7363dac63c97093.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
5 = 2,
x2,
If_i (5 = 3) x3 (If_i (5 = 4) x4 (If_i (5 = 5) x5 (If_i (5 = 6) x6 (If_i (5 = 7) x7 x8)))),
λ x9 x10 . x10 = x5 leaving 2 subgoals.
The subproof is completed by applying unknownprop_b6d5bc91d64e3274cc85bc2a049597cf22bcda6152c18fc84bffaf4e1bea9120.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
5 = 3,
x3,
If_i (5 = 4) x4 (If_i (5 = 5) x5 (If_i (5 = 6) x6 (If_i (5 = 7) x7 x8))),
λ x9 x10 . x10 = x5 leaving 2 subgoals.
The subproof is completed by applying unknownprop_3c68f484705bdee686451aa98debe1c57b9d8d3b0df1b24fadecff9df55960a9.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
5 = 4,
x4,
If_i (5 = 5) x5 (If_i (5 = 6) x6 (If_i (5 = 7) x7 x8)),
λ x9 x10 . x10 = x5 leaving 2 subgoals.
The subproof is completed by applying unknownprop_876d0fa88d786a6d4d32c952c7a4f34a4e3294bd3eb4f448bdff43fe1cebe941.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
5 = 5,
x5,
If_i (5 = 6) x6 (If_i (5 = 7) x7 x8).
Let x9 of type ι → ι → ο be given.
Assume H0: x9 5 5.
The subproof is completed by applying H0.