| pf |
|---|
Let x0 of type ι be given.
Apply H0 with λ x1 . x1 = e6f8c.. (f482f.. x1 4a7ef..) (decode_c (f482f.. x1 (4ae4a.. 4a7ef..))) (2b2e3.. (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 → ο be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Apply unknownprop_a35864772ffa5033a1dab14459dc44213778b4d2960571ac6fb653d49e4b68b5 with x1, x2, x3, x4, x5, λ x6 x7 . e6f8c.. x1 x2 x3 x4 x5 = e6f8c.. 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..)))))).
Apply unknownprop_fde8fc102b9f40461cbdebff1d2da7db6338e2a9b4318ffcb90f7bba078ca0bf with x1, x2, decode_c (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, 2b2e3.. (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, decode_p (f482f.. (e6f8c.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), x5, 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.
■ |
|