| ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10)) ⟶ explicit_Field (ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6) (x6 x1 x1) (x6 x2 x1) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10))))) (x3 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9)))) (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10))))))) ⟶ ∀ x7 : ο . (explicit_Complex (ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6) (λ x8 . x6 (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10)))) x1) (λ x8 . x6 (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9))) x1) (x6 x1 x1) (x6 x2 x1) (x6 x1 x2) (λ x8 x9 . x6 (x3 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x9 = x6 x10 x11))))) (x3 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x9 = x6 x12 x13)))) x10))))) (λ x8 x9 . x6 (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x9 = x6 x10 x11))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x9 = x6 x12 x13)))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x9 = x6 x12 x13)))) x10)))) (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x9 = x6 x10 x11))))))) ⟶ ((∀ x8 . x8 ∈ x0 ⟶ x6 x8 x1 = x8) ⟶ ∀ x8 : ο . ((∀ x9 : ο . ((∀ x10 : ο . ((∀ x11 : ο . ((∀ x12 : ο . (x0 ⊆ ReplSep2 x0 (λ x13 . x0) (λ x13 x14 . True) x6 ⟶ (∀ x13 . x13 ∈ x0 ⟶ prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x13 = x6 x15 x16))) = x13) ⟶ x12) ⟶ x12) ⟶ x6 x1 x1 = x1 ⟶ x11) ⟶ x11) ⟶ x6 x2 x1 = x2 ⟶ x10) ⟶ x10) ⟶ (∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x10 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x11 = x6 x13 x14))))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x10 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x10 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x11 = x6 x15 x16)))) x13)))) = x3 x10 x11) ⟶ x9) ⟶ x9) ⟶ (∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 (x3 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x9 = x6 x12 x13)))) (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x10 = x6 x12 x13))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (x9 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x9 = x6 x14 x15)))) x12))) (prim0 (λ x12 . and (x12 ∈ x0) (x10 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x10 = x6 x14 x15)))) x12)))))) (x3 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x9 = x6 x12 x13)))) (prim0 (λ x12 . and (x12 ∈ x0) (x10 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x10 = x6 x14 x15)))) x12)))) (x4 (prim0 (λ x12 . and (x12 ∈ x0) (x9 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x9 = x6 x14 x15)))) x12))) (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x10 = x6 x12 x13)))))) = x4 x9 x10) ⟶ x8) ⟶ x8) ⟶ x7) ⟶ x7 |
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