Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = e0718.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (e3162.. (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 → ι be given.
Apply unknownprop_c7497c326e0bcb75fa2cc505e6dafed2f342db0b83093fa52226d04b865b9a91 with
x1,
x2,
x3,
λ x4 x5 . e0718.. x1 x2 x3 = e0718.. x4 (decode_c (f482f.. (e0718.. x1 x2 x3) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (e0718.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_84525c9fd7a8a2bd4297ba8d1487280b7045f83e5da16d8bd0ea1c8888bd48bd with
x1,
x2,
decode_c (f482f.. (e0718.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
e3162.. (f482f.. (e0718.. 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_71d4b3d2b3a5f29d2cd05a29c47b2f0fa1a64aff8b5bd681eeb78733ed987d9d 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_b1715816bd75ab55604fa7666530ab99e6bf52403540cf592ed4c4fda9cb0db1 with x1, x2, x3.