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Proofgold Proof

pf
Let x0 of type ι((ιο) → ο) → (ιιο) → (ιο) → ι be given.
Let x1 of type ι be given.
Let x2 of type (ιο) → ο be given.
Let x3 of type ιιο be given.
Let x4 of type ιο be given.
Assume H0: ∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7prim1 x7 x1)iff (x2 x6) (x5 x6))∀ x6 : ι → ι → ο . (∀ x7 . prim1 x7 x1∀ x8 . prim1 x8 x1iff (x3 x7 x8) (x6 x7 x8))∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1iff (x4 x8) (x7 x8))x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4.
Apply unknownprop_53a1434582c46791d97bf0b29daf1e96260f65f75da341b82fe60b82f00728d7 with x1, x2, x3, x4, λ x5 x6 . x0 x5 (decode_c (f482f.. (30bff.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (30bff.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (30bff.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4.
Apply H0 with decode_c (f482f.. (30bff.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)), 2b2e3.. (f482f.. (30bff.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))), decode_p (f482f.. (30bff.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
Let x5 of type ιο be given.
Assume H1: ∀ x6 . x5 x6prim1 x6 x1.
Apply unknownprop_7708a5a648779c332bd616f6e4513a6548347153ed171f25a7c039b600789f31 with x1, x2, x3, x4, x5, λ x6 x7 : ο . iff (x2 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x5.
Let x5 of type ι be given.
Assume H1: prim1 x5 x1.
Let x6 of type ι be given.
Assume H2: prim1 x6 x1.
Apply unknownprop_580e8f89400098eafc477e78627cca2cb91e5401e413a05dcb445fa113c00c84 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x3 x5 x6) x7 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 x5 x6.
Let x5 of type ι be given.
Assume H1: prim1 x5 x1.
Apply unknownprop_26c09a5fb4cb36f7b0ddea94b180a8c22b92587770fba43cdead9a6362679f2e with x1, x2, x3, x4, x5, λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x4 x5.