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.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
8,
λ x8 . If_i (x8 = 0) x0 (If_i (x8 = 1) x1 (If_i (x8 = 2) x2 (If_i (x8 = 3) x3 (If_i (x8 = 4) x4 (If_i (x8 = 5) x5 (If_i (x8 = 6) x6 x7)))))),
6,
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_e6d2a608c5848e98fa602b17a87ba3dd75f325666e5beaf08219a20e80897eb2.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
6 = 0,
x0,
If_i (6 = 1) x1 (If_i (6 = 2) x2 (If_i (6 = 3) x3 (If_i (6 = 4) x4 (If_i (6 = 5) x5 (If_i (6 = 6) x6 x7))))),
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_1add60ac1bb26fce502caf38e7c2d1cedc696f2b1b9ca8289d900bc48bbb4601.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
6 = 1,
x1,
If_i (6 = 2) x2 (If_i (6 = 3) x3 (If_i (6 = 4) x4 (If_i (6 = 5) x5 (If_i (6 = 6) x6 x7)))),
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_1cf2bad1b6260ebc93d971b9afbe41477101c598b232cadbbf721e7e8d169e53.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
6 = 2,
x2,
If_i (6 = 3) x3 (If_i (6 = 4) x4 (If_i (6 = 5) x5 (If_i (6 = 6) x6 x7))),
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_faf467f7f12721a64c9d3a4d80f1c0dc0e349cb3abfd5fb903e8ef11dc2a0f1c.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
6 = 3,
x3,
If_i (6 = 4) x4 (If_i (6 = 5) x5 (If_i (6 = 6) x6 x7)),
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_b3ec9bbbe51cc80450bef2e566c6e2c57f02b88ad6456ac2b606a65ba26bd8af.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
6 = 4,
x4,
If_i (6 = 5) x5 (If_i (6 = 6) x6 x7),
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_41c3a613b74d57a14c405ccfe7da39c5edea096a2f2404d400607529687a6d9c.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
6 = 5,
x5,
If_i (6 = 6) x6 x7,
λ x8 x9 . x9 = x6 leaving 2 subgoals.
The subproof is completed by applying unknownprop_b14ea6afaa39c452b8b24e1418d632500fb837d461f3d3d05f85159bffc766b6.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
6 = 6,
x6,
x7.
Let x8 of type ι → ι → ο be given.
Assume H0: x8 6 6.
The subproof is completed by applying H0.