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Proofgold Proof

pf
Let x0 of type ι((ιο) → ο) → (ιιι) → (ιο) → ιι be given.
Let x1 of type ι be given.
Let x2 of type (ιο) → ο be given.
Let x3 of type ιιι be given.
Let x4 of type ιο be given.
Let x5 of type ι be given.
Assume H0: ∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8prim1 x8 x1)iff (x2 x7) (x6 x7))∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1∀ x9 . prim1 x9 x1x3 x8 x9 = x7 x8 x9)∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1iff (x4 x9) (x8 x9))x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5.
Apply unknownprop_65cce1600a86bdb4fcc47c3f21cd540289b2d8a67dba9d2cfdb16c7b60cd3592 with x1, x2, x3, x4, x5, λ x6 x7 . x0 x6 (decode_c (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4 x5.
Apply unknownprop_d541830b9bb76016fdfd9d4a39b99cfc03581aed7733587f376a6613a3d27e18 with x1, x2, x3, x4, x5, λ x6 x7 . x0 x1 (decode_c (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 = x0 x1 x2 x3 x4 x5.
Apply H0 with decode_c (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), e3162.. (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), decode_p (f482f.. (bebf6.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
Let x6 of type ιο be given.
Assume H1: ∀ x7 . x6 x7prim1 x7 x1.
Apply unknownprop_893520f3075c4d3a8ba22723b37a813951891a352483f9ee1c79192185721ed8 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.
The subproof is completed by applying unknownprop_d00271e3409a7f60fd60ced864a095054ad7fb1dd9954a22fb8f485fbf2f84a4 with x1, x2, x3, x4, x5.
Let x6 of type ι be given.
Assume H1: prim1 x6 x1.
Apply unknownprop_8472672de8e4a6002250f4bca01a91b0df686dd5f362cb55afa19360ce15f05d 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.