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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 ιι be given.
Let x4 of type ιιο be given.
Let x5 of type ι be given.
Assume H0: x0 = pack_c_u_r_e x1 x2 x3 x4 x5.
Let x6 of type ι be given.
Assume H1: x6x1.
Apply H0 with λ x7 x8 . x3 x6 = ap (ap x8 2) x6.
Apply tuple_5_2_eq with x1, encode_c x1 x2, lam x1 x3, encode_r x1 x4, x5, λ x7 x8 . x3 x6 = ap x8 x6.
Let x7 of type ιιο be given.
Apply beta with x1, x3, x6, λ x8 x9 . x7 x9 x8.
The subproof is completed by applying H1.