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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 ιο be given.
Assume H0: x0 = pack_c_u_r_p x1 x2 x3 x4 x5.
Let x6 of type ι be given.
Assume H1: x6x1.
Let x7 of type ι be given.
Assume H2: x7x1.
Apply H0 with λ x8 x9 . x4 x6 x7 = decode_r (ap x9 3) x6 x7.
Apply tuple_5_3_eq with x1, encode_c x1 x2, lam x1 x3, encode_r x1 x4, Sep x1 x5, λ x8 x9 . x4 x6 x7 = decode_r x9 x6 x7.
Let x8 of type οοο be given.
Apply decode_encode_r with x1, x4, x6, x7, λ x9 x10 : ο . x8 x10 x9 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.