| ∀ 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_Reals {x7 ∈ ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6|x6 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) x1 = x7} (x6 x1 x1) (x6 x2 x1) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (x3 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ 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 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))) (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))))) (λ x7 x8 . x5 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) |
|