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Proofgold Proof

pf
Let x0 of type ι(ιιι) → ο be given.
Let x1 of type ι be given.
Let x2 of type ιιι be given.
Assume H0: ∀ x3 : ι → ι → ι . (∀ x4 . x4x1∀ x5 . x5x1x2 x4 x5 = x3 x4 x5)x0 x1 x3 = x0 x1 x2.
Apply pack_b_0_eq2 with x1, x2, λ x3 x4 . x0 x3 (decode_b (ap (pack_b x1 x2) 1)) = x0 x1 x2.
Apply H0 with decode_b (ap (pack_b x1 x2) 1).
Let x3 of type ι be given.
Assume H1: x3x1.
Let x4 of type ι be given.
Assume H2: x4x1.
Apply pack_b_1_eq2 with x1, x2, x3, x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.