Let x0 of type ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → (ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Assume H0:
∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5.
Apply unknownprop_ae678ad878bbb814c7a7959a43e7a6938c60fbfc51ab3f6fdd661988d67e7f0a with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x6 (decode_c (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = x0 x1 x2 x3 x4 x5.
Apply H0 with
decode_c (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)),
f482f.. (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))),
decode_p (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))),
decode_p (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) leaving 4 subgoals.
Let x6 of type ι → ο be given.
Assume H1:
∀ x7 . x6 x7 ⟶ prim1 x7 x1.
Apply unknownprop_e76823d36ee6db8ba833b34f42a40774cc3044020361dd9910febc7213bfae10 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x2 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x6.
The subproof is completed by applying unknownprop_5e1f761718d285321c4cb3dc55f0919bfa4a4030aa97d5da2bb3f8a34962fa42 with x1, x2, x3, x4, x5.
Let x6 of type ι be given.
Apply unknownprop_0aba2d0795a56205879344d672f508bd17da6911a38e8280a31351ebdd8657c2 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x4 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x4 x6.
Let x6 of type ι be given.
Apply unknownprop_1c902ef957d0386ad522c8de47ba741a02d9b45b3972360fdd4aa7b83a097539 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x5 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x5 x6.