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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιι be given.
Let x2 of type ιιο be given.
Let x3 of type ι be given.
Assume H0: struct_u_r_e (pack_u_r_e x0 x1 x2 x3).
Apply H0 with λ x4 . x4 = pack_u_r_e x0 x1 x2 x3∀ x5 . x5x0x1 x5x0 leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type ιι be given.
Assume H1: ∀ x6 . x6x4x5 x6x4.
Let x6 of type ιιο be given.
Let x7 of type ι be given.
Assume H2: x7x4.
Assume H3: pack_u_r_e x4 x5 x6 x7 = pack_u_r_e x0 x1 x2 x3.
Apply pack_u_r_e_inj with x4, x0, x5, x1, x6, x2, x7, x3, ∀ x8 . x8x0x1 x8x0 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H4: and (and (x4 = x0) (∀ x8 . x8x4x5 x8 = x1 x8)) (∀ x8 . x8x4∀ x9 . x9x4x6 x8 x9 = x2 x8 x9).
Apply H4 with x7 = x3∀ x8 . x8x0x1 x8x0.
Assume H5: and (x4 = x0) (∀ x8 . x8x4x5 x8 = x1 x8).
Apply H5 with (∀ x8 . x8x4∀ x9 . x9x4x6 x8 x9 = x2 x8 x9)x7 = x3∀ x8 . x8x0x1 x8x0.
Assume H6: x4 = x0.
Assume H7: ∀ x8 . x8x4x5 x8 = x1 x8.
Assume H8: ∀ x8 . x8x4∀ x9 . x9x4x6 x8 x9 = x2 x8 x9.
Assume H9: x7 = x3.
Apply H6 with λ x8 x9 . ∀ x10 . x10x8x1 x10x8.
Let x8 of type ι be given.
Assume H10: x8x4.
Apply H7 with x8, λ x9 x10 . x9x4 leaving 2 subgoals.
The subproof is completed by applying H10.
Apply H1 with x8.
The subproof is completed by applying H10.
Let x4 of type ιιο be given.
Assume H1: x4 (pack_u_r_e x0 x1 x2 x3) (pack_u_r_e x0 x1 x2 x3).
The subproof is completed by applying H1.