Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 48567.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Apply unknownprop_443af384f5a766563c87fe1d5f5df83d020f061721e547989a9faf36c7e3644e with
x1,
x2,
x3,
x4,
λ x5 x6 . 48567.. x1 x2 x3 x4 = 48567.. x5 (e3162.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_b6909c5dff1fb43ebdc001458c5897fbb3ef3b47c78c20e1838eb8e968585acb with
x1,
x2,
x3,
x4,
λ x5 x6 . 48567.. x1 x2 x3 x4 = 48567.. x1 (e3162.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5.
Apply unknownprop_0d3ca2d7bb2af0fd04198567bf6daa6bf79bec973ffea09106576dbec871a9b3 with
x1,
x2,
e3162.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
f482f.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_e872f769d2f751d5ba4c285643abe39ba33ed9f3bd7608e4c63b386dc1f5861a with x1, x2, x3, x4.
The subproof is completed by applying unknownprop_aa5c741718ec84d60101c87f4b6d2bcc1b84ecd0ab92ad5cbef8a4e52fd8c3ad with x1, x2, x3, x4.