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Proofgold Proof

pf
Let x0 of type ι(ιιιι) → ιιι be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ι → ι → ι . (∀ x4 . x4x1x2 x4 = x3 x4)x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Apply In_rec_G_iii_f with x0, x1, In_rec_iii x0 x1, x0 x1 (In_rec_iii x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply In_rec_G_iii_In_rec_iii with x0, x1.
The subproof is completed by applying H0.
Apply In_rec_G_iii_In_rec_iii_d with x0, x1.
The subproof is completed by applying H0.