Let x0 of type ι → ((ι → ο) → ο) → (ι → ι → ο) → (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 → ο 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 → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ ∀ 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_a35864772ffa5033a1dab14459dc44213778b4d2960571ac6fb653d49e4b68b5 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x6 (decode_c (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = x0 x1 x2 x3 x4 x5.
Apply H0 with
decode_c (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))),
decode_p (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))),
decode_p (f482f.. (e6f8c.. 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_215f643f6fc971f2151839e9b1f3fc5cd98d7a85ab03a836c327d1ac105705e3 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.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_45b26e282902feb9824e8d0271219182843ca6faf3e3511fed1a715638410ab7 with
x1,
x2,
x3,
x4,
x5,
x6,
x7,
λ x8 x9 : ο . iff (x3 x6 x7) x8 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 x6 x7.
Let x6 of type ι be given.
Apply unknownprop_cdb10cf923c4d6c055b970eb6e14e3628babfb72f3289e5087d5b9ba27a5ab78 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_66e0f553bf60528398e00ac18a967472fadc05bac9798988041c8b528ff461c2 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.