| ∀ 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)) ⟶ ∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ ∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 (x3 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (x3 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x7 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x7 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 (x3 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (x3 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 (x3 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (x3 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x7 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x7 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 (x3 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (x3 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) = x6 x11 x13) ⟶ x12) ⟶ x12))))) = x6 (x3 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x7 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))))) (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x7 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))))) = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x7 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))))) (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x7 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))))) = x6 x11 x13) ⟶ x12) ⟶ x12)))) (x3 (prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x7 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x7 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x7 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x7 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x7 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x7 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))))) (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x7 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x7 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x7 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x7 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x7 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x7 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x7 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x7 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x7 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))))) (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x7 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x7 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x7 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) |
|