Proofgold Signed Transaction

Param explicit_Field^{explicit_Field} : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param explicit_Field_minus^{explicit_Field_minus} : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι
Definition and^and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known explicit_Field_E^{explicit_Field_E} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ο . (explicit_Field x0 x1 x2 x3 x4 ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x3 x6 x7 ∈ x0) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x3 x6 (x3 x7 x8) = x3 (x3 x6 x7) x8) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x3 x6 x7 = x3 x7 x6) ⟶ x1 ∈ x0 ⟶ (∀ x6 . x6 ∈ x0 ⟶ x3 x1 x6 = x6) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∃ x7 . and (x7 ∈ x0) (x3 x6 x7 = x1)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 x6 x7 ∈ x0) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 x6 (x4 x7 x8) = x4 (x4 x6 x7) x8) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 x6 x7 = x4 x7 x6) ⟶ x2 ∈ x0 ⟶ (x2 = x1 ⟶ ∀ x6 : ο . x6) ⟶ (∀ x6 . x6 ∈ x0 ⟶ x4 x2 x6 = x6) ⟶ (∀ x6 . x6 ∈ x0 ⟶ (x6 = x1 ⟶ ∀ x7 : ο . x7) ⟶ ∃ x7 . and (x7 ∈ x0) (x4 x6 x7 = x2)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 x6 (x3 x7 x8) = x3 (x4 x6 x7) (x4 x6 x8)) ⟶ x5) ⟶ explicit_Field x0 x1 x2 x3 x4 ⟶ x5
Known explicit_Field_minus_clos^{explicit_Field_minus_clos} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x5 ∈ x0
Known explicit_Field_minus_zero^{explicit_Field_minus_zero} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x1 = x1
Known explicit_Field_minus_invol^{explicit_Field_minus_invol} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x5) = x5
Known explicit_Field_minus_L^{explicit_Field_minus_L} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ x3 (explicit_Field_minus x0 x1 x2 x3 x4 x5) x5 = x1
Known explicit_Field_minus_R^{explicit_Field_minus_R} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ x3 x5 (explicit_Field_minus x0 x1 x2 x3 x4 x5) = x1
Known explicit_Field_dist_R^{explicit_Field_dist_R} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 (x3 x5 x6) x7 = x3 (x4 x5 x7) (x4 x6 x7)
Known explicit_Field_minus_plus_dist^{explicit_Field_minus_plus_dist} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (x3 x5 x6) = x3 (explicit_Field_minus x0 x1 x2 x3 x4 x5) (explicit_Field_minus x0 x1 x2 x3 x4 x6)
Known explicit_Field_minus_mult_L^{explicit_Field_minus_mult_L} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ x4 (explicit_Field_minus x0 x1 x2 x3 x4 x5) x6 = explicit_Field_minus x0 x1 x2 x3 x4 (x4 x5 x6)
Known explicit_Field_minus_mult_R^{explicit_Field_minus_mult_R} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ x4 x5 (explicit_Field_minus x0 x1 x2 x3 x4 x6) = explicit_Field_minus x0 x1 x2 x3 x4 (x4 x5 x6)
Known explicit_Field_zero_multL^{explicit_Field_zero_multL} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ x4 x1 x5 = x1
Known explicit_Field_zero_multR^{explicit_Field_zero_multR} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . x5 ∈ x0 ⟶ x4 x5 x1 = x1
Known explicit_Field_minus_one_In^{explicit_Field_minus_one_In} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x2 ∈ x0
Theorem c888a.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 : ο . ((∀ x6 . x6 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x6 ∈ x0) ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x1 = x1 ⟶ (∀ x6 . x6 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x6) = x6) ⟶ (∀ x6 . x6 ∈ x0 ⟶ x3 (explicit_Field_minus x0 x1 x2 x3 x4 x6) x6 = x1) ⟶ (∀ x6 . x6 ∈ x0 ⟶ x3 x6 (explicit_Field_minus x0 x1 x2 x3 x4 x6) = x1) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 (x3 x6 x7) x8 = x3 (x4 x6 x8) (x4 x7 x8)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (x3 x6 x7) = x3 (explicit_Field_minus x0 x1 x2 x3 x4 x6) (explicit_Field_minus x0 x1 x2 x3 x4 x7)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 (explicit_Field_minus x0 x1 x2 x3 x4 x6) x7 = explicit_Field_minus x0 x1 x2 x3 x4 (x4 x6 x7)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 x6 (explicit_Field_minus x0 x1 x2 x3 x4 x7) = explicit_Field_minus x0 x1 x2 x3 x4 (x4 x6 x7)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ x4 x1 x6 = x1) ⟶ (∀ x6 . x6 ∈ x0 ⟶ x4 x6 x1 = x1) ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x2 ∈ x0 ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 x6 (x4 x7 x8) ∈ x0) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x3 (x3 x6 x7) (x3 x8 x9) = x3 (x3 x6 x9) (x3 x7 x8)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x3 (x3 x6 x7) (x3 x8 x9) = x3 (x3 x6 x8) (x3 x7 x9)) ⟶ x5) ⟶ x5
Param explicit_Reals^{explicit_Reals} : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Param ReplSep2^ReplSep2 : ι → (ι → ι) → (ι → ι → ο) → CT2 ι
Definition True^True := ∀ x0 : ο . x0 ⟶ x0
Param Sep^Sep : ι → (ι → ο) → ι
Param explicit_OrderedField^{explicit_OrderedField} : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Param lt^lt : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ι → ι → ο
Param natOfOrderedField_p^{natOfOrderedField_p} : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ι → ο
Param setexp^setexp : ι → ι → ι
Param ap^ap : ι → ι → ι
Known explicit_Reals_E^{explicit_Reals_E} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ο . (explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ explicit_OrderedField x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ lt x0 x1 x2 x3 x4 x5 x1 x7 ⟶ x5 x1 x8 ⟶ ∃ x9 . and (x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) (x5 x8 (x4 x9 x7))) ⟶ (∀ x7 . x7 ∈ setexp x0 (Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ ∀ x8 . x8 ∈ setexp x0 (Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ (∀ x9 . x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5) ⟶ and (and (x5 (ap x7 x9) (ap x8 x9)) (x5 (ap x7 x9) (ap x7 (x3 x9 x2)))) (x5 (ap x8 (x3 x9 x2)) (ap x8 x9))) ⟶ ∃ x9 . and (x9 ∈ x0) (∀ x11 . x11 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5) ⟶ and (x5 (ap x7 x11) x9) (x5 x9 (ap x8 x11)))) ⟶ x6) ⟶ explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ x6
Param iff^iff : ο → ο → ο
Param or^or : ο → ο → ο
Known explicit_OrderedField_E^{explicit_OrderedField_E} : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ο . (explicit_OrderedField x0 x1 x2 x3 x4 x5 ⟶ explicit_Field x0 x1 x2 x3 x4 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x5 x7 x8 ⟶ x5 x8 x9 ⟶ x5 x7 x9) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ iff (and (x5 x7 x8) (x5 x8 x7)) (x7 = x8)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ or (x5 x7 x8) (x5 x8 x7)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x5 x7 x8 ⟶ x5 (x3 x7 x9) (x3 x8 x9)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x5 x1 x7 ⟶ x5 x1 x8 ⟶ x5 x1 (x4 x7 x8)) ⟶ x6) ⟶ explicit_OrderedField x0 x1 x2 x3 x4 x5 ⟶ x6
Known SepI^SepI : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . x2 ∈ x0 ⟶ x1 x2 ⟶ x2 ∈ Sep x0 x1
Known Eps_i_ex^Eps_i_ex : ∀ x0 : ι → ο . (∃ x1 . x0 x1) ⟶ x0 (prim0 x0)
Known andI^andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Known ReplSep2E_impred^{ReplSep2E_impred} : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ι → ι . ∀ x4 . x4 ∈ ReplSep2 x0 x1 x2 x3 ⟶ ∀ x5 : ο . (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x1 x6 ⟶ x2 x6 x7 ⟶ x4 = x3 x6 x7 ⟶ x5) ⟶ x5
Known ReplSep2I^ReplSep2I : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ι → ι . ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x1 x4 ⟶ x2 x4 x5 ⟶ x3 x4 x5 ∈ ReplSep2 x0 x1 x2 x3
Known TrueI^TrueI : True
Theorem 89287.. : ∀ 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 : ο . ((∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x6 x8 x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 : ι → ο . (∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x8 = x6 x10 x11 ⟶ x9 (x6 x10 x11)) ⟶ x9 x8) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x6 x8 x9 = x6 x11 x12))) = x8) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x8 x9 = x6 x13 x14)))) x11)) = x9) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10))) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9)) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ x8 = x6 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10)))) ⟶ (∀ x8 . x8 ∈ x0 ⟶ x6 x8 x1 ∈ {x9 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6|x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12)))) x1 = x9}) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12))) = prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))) ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11)) = prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)) ⟶ x8 = x9) ⟶ x6 x1 x1 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ x6 x2 x1 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x8 x9 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x10 x11 = x6 x13 x14))))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x6 x8 x9 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x6 x10 x11 = x6 x15 x16)))) x13)))) = x6 (x3 x8 x10) (x3 x9 x11)) ⟶ (∀ 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 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))) (x3 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))) = x6 (x3 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))) (x3 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11))))) ⟶ (∀ 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 (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)))) ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . 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 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x6 (x3 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x8 = x6 x15 x16)))) (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x9 = x6 x15 x16))))) (x3 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x8 = x6 x17 x18)))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x9 = x6 x17 x18)))) x15)))) = x6 x11 x12))) = x3 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14))))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x8 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x9 = x6 x15 x16)))) x13)))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 (x3 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x8 = x6 x17 x18)))) (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x9 = x6 x17 x18))))) (x3 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∃ x20 . and (x20 ∈ x0) (x8 = x6 x19 x20)))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∃ x20 . and (x20 ∈ x0) (x9 = x6 x19 x20)))) x17)))) = x6 x13 x14)))) x11)) = x3 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x8 x9 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x10 x11 = x6 x13 x14))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x6 x8 x9 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x6 x10 x11 = x6 x15 x16)))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x8 x9 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x6 x10 x11 = x6 x15 x16)))) x13)))) (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x6 x8 x9 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 x10 x11 = x6 x13 x14)))))) = x6 (x3 (x4 x8 x10) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 x9 x11))) (x3 (x4 x8 x11) (x4 x9 x10))) ⟶ (∀ 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 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12)))))) = x6 (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) 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))))) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ 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))))) ∈ x0) ⟶ (∀ 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 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)))))) ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . 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 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x6 (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x8 = x6 x15 x16)))) (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x9 = x6 x15 x16))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x8 = x6 x17 x18)))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x9 = x6 x17 x18)))) x15)))))) (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x8 = x6 x15 x16)))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x9 = x6 x17 x18)))) x15)))) (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x8 = x6 x17 x18)))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x9 = x6 x15 x16)))))) = x6 x11 x12))) = x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x8 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x9 = x6 x15 x16)))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x9 = x6 x15 x16)))) x13)))) (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x8 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x6 (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x8 = x6 x17 x18)))) (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x9 = x6 x17 x18))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∃ x20 . and (x20 ∈ x0) (x8 = x6 x19 x20)))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∃ x20 . and (x20 ∈ x0) (x9 = x6 x19 x20)))) x17)))))) (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x8 = x6 x17 x18)))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∃ x20 . and (x20 ∈ x0) (x9 = x6 x19 x20)))) x17)))) (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∃ x20 . and (x20 ∈ x0) (x8 = x6 x19 x20)))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x9 = x6 x17 x18)))))) = x6 x13 x14)))) x11)) = x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x9 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x9 = x6 x11 x12)))))) ⟶ x7) ⟶ x7