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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type (ιο) → ο be given.
Assume H0: x0 = lam 2 (λ x3 . If_i (x3 = 0) x1 (encode_c x1 x2)).
Apply H0 with λ x3 x4 . x1 = ap x4 0.
Let x3 of type ιιο be given.
The subproof is completed by applying tuple_2_0_eq with x1, encode_c x1 x2, λ x4 x5 . x3 x5 x4.