| ∀ x0 : ι → (ι → ι → ι) → ο . (∀ x1 . ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ∈ x1) ⟶ ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ x2 x4 x5 = x3 x4 x5) ⟶ x0 x1 x3 = x0 x1 x2) ⟶ (∀ x1 . ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ∈ x1) ⟶ x0 x1 x2 ⟶ ∀ x3 . ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ x3 ⟶ ∀ x6 . x6 ∈ x3 ⟶ x4 x5 x6 ∈ x3) ⟶ x0 x3 x4 ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ setprod x1 x3 ⟶ ∀ x7 . x7 ∈ setprod x1 x3 ⟶ lam 2 (λ x9 . If_i (x9 = 0) (x2 (ap x6 0) (ap x7 0)) (x4 (ap x6 1) (ap x7 1))) = x5 x6 x7) ⟶ x0 (setprod x1 x3) x5) ⟶ ∀ x1 : ο . (∀ x2 : ι → ι → ι . (∀ x3 : ο . (∀ x4 : ι → ι → ι . (∀ x5 : ο . (∀ x6 : ι → ι → ι . (∀ x7 : ο . (∀ x8 : ι → ι → ι → ι → ι → ι . MetaCat_product_constr_p (λ x9 . and (struct_b x9) (unpack_b_o x9 x0)) MagmaHom struct_id struct_comp x2 x4 x6 x8 ⟶ x7) ⟶ x7) ⟶ x5) ⟶ x5) ⟶ x3) ⟶ x3) ⟶ x1) ⟶ x1 |
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