Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 36e8b.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (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 → ο be given.
Apply unknownprop_f3c4051a2e82c5c097e96523837f5f49627024088d43123293e7dcdfed200e03 with
x1,
x2,
x3,
λ x4 x5 . 36e8b.. x1 x2 x3 = 36e8b.. x4 (decode_c (f482f.. (36e8b.. x1 x2 x3) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (36e8b.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_f2908be57ae2a18f212b489d9ec3967b2c1d8c18386b64f151cd1f22fda4c9ba with
x1,
x2,
decode_c (f482f.. (36e8b.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
2b2e3.. (f482f.. (36e8b.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x4 of type ι → ο be given.
Assume H1:
∀ x5 . x4 x5 ⟶ prim1 x5 x1.
Apply unknownprop_3d331d0eaedf4b64c00959d651f2171f5e833837a051ea6a657190c8ede5e40c with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x4.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_337868cd85364af324568d79df123fe318bd85bd40be54c846b923343db08c2c with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x4 x5.