Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = fc7e7.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x1 (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 be given.
Apply unknownprop_02cad8e0186a13edac760a40b04d581d34236e30332ea33ec2471a5050e9b8b5 with
x1,
x2,
x3,
λ x4 x5 . fc7e7.. x1 x2 x3 = fc7e7.. x4 (decode_c (f482f.. (fc7e7.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (fc7e7.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_c818bb3f65db2afda9d5df8a91f676a02a4df85e455427cb0105fb9d2950b02c with
x1,
x2,
decode_c (f482f.. (fc7e7.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
f482f.. (f482f.. (fc7e7.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x4 of type ι → ο be given.
Assume H2:
∀ x5 . x4 x5 ⟶ prim1 x5 x1.
Apply unknownprop_c0871275b39d34d2963c3a36a1dfeee6d52fc7b10ea038c0356ce70595fa5b0f with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x4.
The subproof is completed by applying unknownprop_d032a8bd5d30b0278d4b4eaea55e89ad39f6273a17060935741b85f1e05b0ccf with x1, x2, x3.