Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι be given.

Let x3 of type ι → ι be given.

Let x4 of type ι → ο be given.

Let x5 of type ι be given.

Assume H0: x0 = pack_u_u_p_e x1 x2 x3 x4 x5.

Let x6 of type ι be given.

Assume H1: x6 ∈ x1.

Apply H0 with λ x7 x8 . x4 x6 = decode_p (ap x8 3) x6.

Apply tuple_5_3_eq with x1, lam x1 x2, lam x1 x3, Sep x1 x4, x5, λ x7 x8 . x4 x6 = decode_p x8 x6.

Let x7 of type ο → ο → ο be given.

Apply decode_encode_p with x1, x4, x6, λ x8 x9 : ο . x7 x9 x8.

The subproof is completed by applying H1.

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Proofgold Proof