Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ι → ι be given.

Let x4 of type ι → ι → ο be given.

Assume H0: x0 = pack_b_b_r x1 x2 x3 x4.

Apply H0 with λ x5 x6 . x1 = ap x6 0.

Let x5 of type ι → ι → ο be given.

The subproof is completed by applying tuple_4_0_eq with x1, encode_b x1 x2, encode_b x1 x3, encode_r x1 x4, λ x6 x7 . x5 x7 x6.

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Proofgold Proof