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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type (ιο) → ο be given.
Let x2 of type ιι be given.
Assume H0: ∀ x3 . x3x0x2 x3x0.
Let x3 of type ιιο be given.
Let x4 of type ι be given.
Assume H1: x4x0.
Let x5 of type ιο be given.
Assume H2: ∀ x6 . ∀ x7 : (ι → ο) → ο . ∀ x8 : ι → ι . (∀ x9 . x9x6x8 x9x6)∀ x9 : ι → ι → ο . ∀ x10 . x10x6x5 (pack_c_u_r_e x6 x7 x8 x9 x10).
Apply H2 with x0, x1, x2, x3, x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.