| ∀ 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 x6 . MagmaHom (pack_b x1 x2) (pack_b x3 x4) x5 ⟶ MagmaHom (pack_b x1 x2) (pack_b x3 x4) x6 ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ {x9 ∈ x1|ap x5 x9 = ap x6 x9} ⟶ ∀ x9 . x9 ∈ {x10 ∈ x1|ap x5 x10 = ap x6 x10} ⟶ x2 x8 x9 = x7 x8 x9) ⟶ x0 {x8 ∈ x1|ap x5 x8 = ap x6 x8} x7) ⟶ ∀ x1 : ο . (∀ x2 : ι → ι → ι → ι → ι . (∀ x3 : ο . (∀ x4 : ι → ι → ι → ι → ι . (∀ x5 : ο . (∀ x6 : ι → ι → ι → ι → ι → ι → ι . MetaCat_equalizer_struct_p (λ x7 . and (struct_b x7) (unpack_b_o x7 x0)) MagmaHom struct_id struct_comp x2 x4 x6 ⟶ x5) ⟶ x5) ⟶ x3) ⟶ x3) ⟶ x1) ⟶ x1 |
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