Let x0 of type ι → (ι → ι) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι 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 → ι . (∀ x7 . prim1 x7 x1 ⟶ 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_a5b77ba136878bdbfe706eed76ea7282e39a3866bdf5c554238616f635600105 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x6 (f482f.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = x0 x1 x2 x3 x4 x5.
Apply H0 with
f482f.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))),
decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))),
decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) leaving 4 subgoals.
The subproof is completed by applying unknownprop_53dadf2d3c0fd488094990d7abccc6a56a03098a2f8f7bc0ce669abab9acdbd5 with x1, x2, x3, x4, x5.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_362838b47e0c46070dfc6a2cfa51dd0c2ee6c9ee68818dc51a44699e154aed6d 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_a9441044bb881671e9811de1b74ed4f8ec54da1e9895e8c4c33fe5a71700259a 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_2d3e8d3db4db5785e02c095d6a6b685c6a437ffa4f0603b684d98b5ae632b875 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.