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Proofgold Proof

pf
Let x0 of type ι(ιι) → ι be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ι . (∀ x4 . x4x1x2 x4 = x3 x4)x0 x1 x2 = x0 x1 x3.
Apply In_ind with λ x1 . In_rec_i_G x0 x1 (In_rec_i x0 x1).
Let x1 of type ι be given.
Assume H1: ∀ x2 . x2x1In_rec_i_G x0 x2 (In_rec_i x0 x2).
Apply Eps_i_ax with In_rec_i_G x0 x1, x0 x1 (In_rec_i x0).
Apply In_rec_i_G_c with x0, x1, In_rec_i x0.
The subproof is completed by applying H1.