Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 1bcc7.. (f482f.. x1 4a7ef..) (f482f.. (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Apply unknownprop_0cc92ec4e0e6dab19c106c8af8774f1cda73073bc0b40c4ccb1840d7af9b0b0d with
x1,
x2,
x3,
x4,
λ x5 x6 . 1bcc7.. x1 x2 x3 x4 = 1bcc7.. x5 (f482f.. (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_e736d87fb1c82f1653455bc78e80c3d1deb331bc1d61d105d9782506c903a8fd with
x1,
x2,
x3,
x4,
λ x5 x6 . 1bcc7.. x1 x2 x3 x4 = 1bcc7.. x1 (f482f.. (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5.
Apply unknownprop_8a57d94cfd3e3ca01ef4429efb973edd24b85a189b884580feb4d24993794823 with
x1,
x2,
f482f.. (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (1bcc7.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_0fd914315b038e6cc084f062f01503a01c3efa5b54d8e88f9d1216b20fcbcdc3 with x1, x2, x3, x4.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_022211655377b981fe7e19d29dd3c365db553d8685042e45a1cf4cc105d846fc with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x3 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying iff_refl with x3 x5 x6.