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Let x0 of type ι be given.
Apply H0 with λ x1 . x1 = a3459.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x1 (4ae4a.. (4ae4a.. (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.
Let x4 of type ι → ο be given.
Let x5 of type ι be given.
Apply unknownprop_97c6febb4d48ff36e4cb1a67ae96e731bb4d0d88ae631b336ee8d751a8ea3644 with x1, x2, x3, x4, x5, λ x6 x7 . a3459.. x1 x2 x3 x4 x5 = a3459.. x6 (decode_c (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_68fa418e80e05b5f5d85946aaba333bbaea1a45e6bff44a3e7bbfdbb8602422f with x1, x2, x3, x4, x5, λ x6 x7 . a3459.. x1 x2 x3 x4 x5 = a3459.. x1 (decode_c (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6.
Apply unknownprop_aedd4a9fb4e8a0a3fab35d9e740aa14057e2841758c8706c7bf7efe2631e4368 with x1, x2, decode_c (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, 2b2e3.. (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, decode_p (f482f.. (a3459.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), x5 leaving 3 subgoals.
Let x6 of type ι → ο be given.
Assume H2: ∀ x7 . x6 x7 ⟶ prim1 x7 x1. Apply unknownprop_f126e736effd1cf0374523a6b7386d5add53fdd920a5f78d4f4f605963832861 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x2 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H2.
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_3b64a3196710182a4d35cba1546eee2e2f7980f2ed75b429503d9f04f3d32e71 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 H2.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x3 x6 x7.
Let x6 of type ι be given.
Apply unknownprop_a2cc32195c89ba000a0e2e102a49e880cf6082a249cefcf846a21241ed3c6cf3 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x4 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x4 x6.
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