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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 ιιι be given.
Let x3 of type ιιι be given.
Assume H0: ∀ x4 . x4x0∀ x5 . x5x1 x4x2 x4 x5 = x3 x4 x5.
Apply encode_u_ext with x0, λ x4 . lam (x1 x4) (λ x5 . x2 x4 x5), λ x4 . lam (x1 x4) (λ x5 . x3 x4 x5).
Let x4 of type ι be given.
Assume H1: x4x0.
Apply encode_u_ext with x1 x4, λ x5 . x2 x4 x5, λ x5 . x3 x4 x5.
Let x5 of type ι be given.
Assume H2: x5x1 x4.
Apply H0 with x4, x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.