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Let x0 of type ι be given.
Apply H0 with λ x1 . x1 = f4fb4.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (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 be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Apply unknownprop_ae678ad878bbb814c7a7959a43e7a6938c60fbfc51ab3f6fdd661988d67e7f0a with x1, x2, x3, x4, x5, λ x6 x7 . f4fb4.. x1 x2 x3 x4 x5 = f4fb4.. 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..)))))).
Apply unknownprop_bed96d8704c71e6def0db960c954a2d47130cbfcd2b069744b3a4017dfa68dc8 with x1, x2, decode_c (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, f482f.. (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, decode_p (f482f.. (f4fb4.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), x5, 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 H2: ∀ 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 H2.
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 H2.
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 H2.
The subproof is completed by applying iff_refl with x5 x6.
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