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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 ιιι be given.
Let x4 of type ι be given.
Assume H0: x0 = pack_c_b_e x1 x2 x3 x4.
Let x5 of type ι be given.
Assume H1: x5x1.
Let x6 of type ι be given.
Assume H2: x6x1.
Apply H0 with λ x7 x8 . x3 x5 x6 = decode_b (ap x8 2) x5 x6.
Apply tuple_4_2_eq with x1, encode_c x1 x2, encode_b x1 x3, x4, λ x7 x8 . x3 x5 x6 = decode_b x8 x5 x6.
Let x7 of type ιιο be given.
Apply decode_encode_b with x1, x3, x5, x6, λ x8 x9 . x7 x9 x8 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.