Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = d7d7e.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ο be given.
Apply unknownprop_ba81b186b20404f2b184823fc867586e7d7244eedb795612a8200f2a550b9d96 with
x1,
x2,
x3,
x4,
λ x5 x6 . d7d7e.. x1 x2 x3 x4 = d7d7e.. x5 (decode_c (f482f.. (d7d7e.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (d7d7e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (d7d7e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_bace2e922dbce7c1ee37741c103b2b3354e184d717d11b9f56fefce13f159400 with
x1,
x2,
decode_c (f482f.. (d7d7e.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
x3,
e3162.. (f482f.. (d7d7e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
x4,
decode_p (f482f.. (d7d7e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
Let x5 of type ι → ο be given.
Assume H2:
∀ x6 . x5 x6 ⟶ prim1 x6 x1.
Apply unknownprop_7b7686cbecedcd60f8f5fdb253b765355b51e9838870215bb6d8f625abc19e28 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x5.
The subproof is completed by applying unknownprop_da5395658eb11644493773387119e852dc723b35ba38d26d0dcd5c668a45e5db with x1, x2, x3, x4.
Let x5 of type ι be given.
Apply unknownprop_b00f9274fcdc66a19bf75646be0063284f767971ab29262c420369ce1337f459 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x4 x5.