| ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x3 x5 x6) x0) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x3 x5 (x3 x6 x7) = x3 (x3 x5 x6) x7) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = x3 x6 x5) ⟶ prim1 x1 x0 ⟶ (∀ x5 . prim1 x5 x0 ⟶ x3 x1 x5 = x5) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 : ο . (∀ x7 . and (prim1 x7 x0) (x3 x5 x7 = x1) ⟶ x6) ⟶ x6) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x4 x5 x6) x0) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x5 (x4 x6 x7) = x4 (x4 x5 x6) x7) ⟶ prim1 x2 x0 ⟶ (x2 = x1 ⟶ ∀ x5 : ο . x5) ⟶ (∀ x5 . prim1 x5 x0 ⟶ x4 x2 x5 = x5) ⟶ (∀ x5 . prim1 x5 x0 ⟶ x4 x5 x2 = x5) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x5 (x3 x6 x7) = x3 (x4 x5 x6) (x4 x5 x7)) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 (x3 x5 x6) x7 = x3 (x4 x5 x7) (x4 x6 x7)) ⟶ explicit_Ring_with_id x0 x1 x2 x3 x4 |
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