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.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
5,
λ x5 . If_i (x5 = 0) x0 (If_i (x5 = 1) x1 (If_i (x5 = 2) x2 (If_i (x5 = 3) x3 x4))),
4,
λ x5 x6 . x6 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_2731ce1d3f81a6fed1bffece1b3536d39c643b0128067d78b6a1741b66c185c5.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 0,
x0,
If_i (4 = 1) x1 (If_i (4 = 2) x2 (If_i (4 = 3) x3 x4)),
λ x5 x6 . x6 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_eaa778def292ef273cdc44e35415a8a42535318d4e19c13ee6ceed0c5eb3f775.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 1,
x1,
If_i (4 = 2) x2 (If_i (4 = 3) x3 x4),
λ x5 x6 . x6 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_75032dcd8ad59e83bbbd268576bb90fef789394372056ddc79da134e39e13bc4.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 2,
x2,
If_i (4 = 3) x3 x4,
λ x5 x6 . x6 = x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_6e85348d9b8c1714b2cb6d272e0e84b0638dd511839ada963d83f563a6d15dde.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
4 = 3,
x3,
x4.
The subproof is completed by applying unknownprop_6959d9e660b21c56708e454ccc9acedd4faf4caf2ab54adc55f634a87d3efc20.