Let x0 of type ι be given.

Apply H0 with λ x1 . x1 = pack_b_b_r_e_e (ap x1 0) (decode_b (ap x1 1)) (decode_b (ap x1 2)) (decode_r (ap x1 3)) (ap x1 4) (ap x1 5).

Let x1 of type ι be given.

Let x2 of type ι → ι → ι be given.

Assume H1: ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ∈ x1.

Let x3 of type ι → ι → ι be given.

Assume H2: ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ x3 x4 x5 ∈ x1.

Let x4 of type ι → ι → ο be given.

Let x5 of type ι be given.

Assume H3: x5 ∈ x1.

Let x6 of type ι be given.

Assume H4: x6 ∈ x1.

Apply pack_b_b_r_e_e_0_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 . pack_b_b_r_e_e x1 x2 x3 x4 x5 x6 = pack_b_b_r_e_e x7 (decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 1)) (decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 2)) (decode_r (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 3)) (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 4) (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 5).

Apply pack_b_b_r_e_e_4_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 . pack_b_b_r_e_e x1 x2 x3 x4 x5 x6 = pack_b_b_r_e_e x1 (decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 1)) (decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 2)) (decode_r (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 3)) x7 (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 5).

Apply pack_b_b_r_e_e_5_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 . pack_b_b_r_e_e x1 x2 x3 x4 x5 x6 = pack_b_b_r_e_e x1 (decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 1)) (decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 2)) (decode_r (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 3)) x5 x7.

Apply pack_b_b_r_e_e_ext with x1, x2, decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 1), x3, decode_b (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 x6) 2), x4, decode_r (ap (pack_b_b_r_e_e x1 x2 x3 x4 x5 ...) 3), ..., ... leaving 3 subgoals.

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Proofgold Proof