Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
3,
λ x3 . If_i (x3 = 0) x0 (If_i (x3 = 1) x1 x2),
2,
λ x3 x4 . x4 = x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_8b6f282335c44ee7de0d36e0ba760eb1cff3979ce58a84352eb0914ef79ff508.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
2 = 0,
x0,
If_i (2 = 1) x1 x2,
λ x3 x4 . x4 = x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_47a023fb65dad0adf6176d6e56f8225fed35ae41cdd7dbd441c63ff764631416.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
2 = 1,
x1,
x2.
The subproof is completed by applying unknownprop_6cb9d1d6bff551a32dbdd07e389ec1293336d9b518cb846bc58565f53757a830.