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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 ιιο be given.
Let x3 of type ιιο be given.
Let x4 of type ιο be given.
Assume H0: x0 = pack_r_r_p 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_r (ap x8 2) x5 x6.
Apply tuple_4_2_eq with x1, encode_r x1 x2, encode_r x1 x3, Sep x1 x4, λ x7 x8 . x3 x5 x6 = decode_r x8 x5 x6.
Let x7 of type οοο be given.
Apply decode_encode_r with x1, x3, x5, x6, λ x8 x9 : ο . x7 x9 x8 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.