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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: struct_r_r_e x0.
Apply H0 with λ x1 . x1 = pack_r_r_e (ap x1 0) (decode_r (ap x1 1)) (decode_r (ap x1 2)) (ap x1 3).
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 ι be given.
Assume H1: x4x1.
Apply pack_r_r_e_0_eq2 with x1, x2, x3, x4, λ x5 x6 . pack_r_r_e x1 x2 x3 x4 = pack_r_r_e x5 (decode_r (ap (pack_r_r_e x1 x2 x3 x4) 1)) (decode_r (ap (pack_r_r_e x1 x2 x3 x4) 2)) (ap (pack_r_r_e x1 x2 x3 x4) 3).
Apply pack_r_r_e_3_eq2 with x1, x2, x3, x4, λ x5 x6 . pack_r_r_e x1 x2 x3 x4 = pack_r_r_e x1 (decode_r (ap (pack_r_r_e x1 x2 x3 x4) 1)) (decode_r (ap (pack_r_r_e x1 x2 x3 x4) 2)) x5.
Apply pack_r_r_e_ext with x1, x2, decode_r (ap (pack_r_r_e x1 x2 x3 x4) 1), x3, decode_r (ap (pack_r_r_e x1 x2 x3 x4) 2), x4 leaving 2 subgoals.
Let x5 of type ι be given.
Assume H2: x5x1.
Let x6 of type ι be given.
Assume H3: x6x1.
Apply pack_r_r_e_1_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x2 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x2 x5 x6.
Let x5 of type ι be given.
Assume H2: x5x1.
Let x6 of type ι be given.
Assume H3: x6x1.
Apply pack_r_r_e_2_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x3 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x3 x5 x6.