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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: 78340.. x0.
Apply H0 with λ x1 . x1 = ae96b.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Assume H1: ∀ x3 . prim1 x3 x1 ⟶ ∀ x4 . prim1 x4 x1 ⟶ prim1 (x2 x3 x4) x1.
Let x3 of type ι → ι be given.
Assume H2: ∀ x4 . prim1 x4 x1 ⟶ prim1 (x3 x4) x1.
Let x4 of type ι → ο be given.
Let x5 of type ι be given.
Assume H3: prim1 x5 x1.
Apply unknownprop_c6595df75e577325f6baea93390717a343f97a9fd476c933483943d2d9a2bbe3 with x1, x2, x3, x4, x5, λ x6 x7 . ae96b.. x1 x2 x3 x4 x5 = ae96b.. x6 (e3162.. (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))).
Apply unknownprop_f9fc77622b15f09a3ab8db7bdf089cac727018759a0a75628dcab110bd804a03 with x1, x2, x3, x4, x5, λ x6 x7 . ae96b.. x1 x2 x3 x4 x5 = ae96b.. x1 (e3162.. (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6.
Apply unknownprop_1f3d8d734bba6f6a5510269c41c32116e76f9112ad480e26bb39f807335b5676 with x1, x2, e3162.. (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)), x3, f482f.. (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))), x4, decode_p (f482f.. (ae96b.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), x5 leaving 3 subgoals.
The subproof is completed by applying unknownprop_d2b3dd43e8b04e0eadc16b79ca8f94b87da6123c154055fd76e55cc2ac09b8d8 with x1, x2, x3, x4, x5.
The subproof is completed by applying unknownprop_4ad3264601a265494da2dd9b0ceafd6b077384105030ee7c0b42358b7fdeee5a with x1, x2, x3, x4, x5.
Let x6 of type ι be given.
Assume H4: prim1 x6 x1.
Apply unknownprop_06b3722b91b5390f0e11d4476a8b6b89ab28b4dc3efe15570095f3884dd562ab with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x4 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying iff_refl with x4 x6.
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