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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιι be given.
Assume H0: ∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x0.
Let x2 of type ιιι be given.
Assume H1: ∀ x3 . x3x0∀ x4 . x4x0x2 x3 x4x0.
Let x3 of type ιιι be given.
Assume H2: ∀ x4 . x4x0∀ x5 . x5x0x3 x4 x5x0.
Let x4 of type ιο be given.
Assume H3: ∀ x5 . ∀ x6 : ι → ι → ι . (∀ x7 . x7x5∀ x8 . x8x5x6 x7 x8x5)∀ x7 : ι → ι → ι . (∀ x8 . x8x5∀ x9 . x9x5x7 x8 x9x5)∀ x8 : ι → ι → ι . (∀ x9 . x9x5∀ x10 . x10x5x8 x9 x10x5)x4 (pack_b_b_b x5 x6 x7 x8).
Apply H3 with x0, x1, x2, x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.