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 → ο be given.

Let x4 of type ι be given.

Let x5 of type ι be given.

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

Apply H0 with λ x6 x7 . x4 = ap x7 3.

Let x6 of type ι → ι → ο be given.

The subproof is completed by applying tuple_5_3_eq with x1, encode_b x1 x2, encode_r x1 x3, x4, x5, λ x7 x8 . x6 x8 x7.

■

Proofgold Proof