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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 ιο be given.
Let x4 of type ι be given.
Assume H0: x0 = pack_c_p_e x1 x2 x3 x4.
Let x5 of type ιο be given.
Assume H1: ∀ x6 . x5 x6x6x1.
Apply H0 with λ x6 x7 . x2 x5 = decode_c (ap x7 1) x5.
Apply tuple_4_1_eq with x1, encode_c x1 x2, Sep x1 x3, x4, λ x6 x7 . x2 x5 = decode_c x7 x5.
Let x6 of type οοο be given.
Apply decode_encode_c with x1, x2, x5, λ x7 x8 : ο . x6 x8 x7.
The subproof is completed by applying H1.