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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type (ιο) → ο be given.
Let x3 of type ιι be given.
Let x4 of type ιο be given.
Let x5 of type ι be given.
Assume H0: x0 = pack_c_u_p_e x1 x2 x3 x4 x5.
Let x6 of type ι be given.
Assume H1: x6x1.
Apply H0 with λ x7 x8 . x4 x6 = decode_p (ap x8 3) x6.
Apply tuple_5_3_eq with x1, encode_c x1 x2, lam x1 x3, Sep x1 x4, x5, λ x7 x8 . x4 x6 = decode_p x8 x6.
Let x7 of type οοο be given.
Apply decode_encode_p with x1, x4, x6, λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying H1.