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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: a4680.. x0.
Apply H0 with λ x1 . x1 = ae02b.. (f482f.. x1 4a7ef..) (f482f.. (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 → ι be given.
Assume H1: ∀ x3 . prim1 x3 x1 ⟶ prim1 (x2 x3) x1.
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_a5b77ba136878bdbfe706eed76ea7282e39a3866bdf5c554238616f635600105 with x1, x2, x3, x4, x5, λ x6 x7 . ae02b.. x1 x2 x3 x4 x5 = ae02b.. x6 (f482f.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))).
Apply unknownprop_576bba5a78e6ba04c7aca824c52c3c1dd0865a228ecfaec2ee69e29d83d10a25 with x1, x2, f482f.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, 2b2e3.. (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), x5, decode_p (f482f.. (ae02b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) leaving 4 subgoals.
The subproof is completed by applying unknownprop_53dadf2d3c0fd488094990d7abccc6a56a03098a2f8f7bc0ce669abab9acdbd5 with x1, x2, x3, x4, x5.
Let x6 of type ι be given.
Assume H2: prim1 x6 x1.
Let x7 of type ι be given.
Assume H3: prim1 x7 x1.
Apply unknownprop_362838b47e0c46070dfc6a2cfa51dd0c2ee6c9ee68818dc51a44699e154aed6d 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.
Assume H2: prim1 x6 x1.
Apply unknownprop_a9441044bb881671e9811de1b74ed4f8ec54da1e9895e8c4c33fe5a71700259a 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.
Assume H2: prim1 x6 x1.
Apply unknownprop_2d3e8d3db4db5785e02c095d6a6b685c6a437ffa4f0603b684d98b5ae632b875 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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