Proofgold Asset

Param explicit_Field : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param explicit_Field_minus : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι
Definition and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known explicit_Field_E : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ο . (explicit_Field x0 x1 x2 x3 x4 ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ prim1 (x3 x6 x7) x0) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x3 x6 (x3 x7 x8) = x3 (x3 x6 x7) x8) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x3 x6 x7 = x3 x7 x6) ⟶ prim1 x1 x0 ⟶ (∀ x6 . prim1 x6 x0 ⟶ x3 x1 x6 = x6) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 : ο . (∀ x8 . and (prim1 x8 x0) (x3 x6 x8 = x1) ⟶ x7) ⟶ x7) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ prim1 (x4 x6 x7) x0) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x4 x6 (x4 x7 x8) = x4 (x4 x6 x7) x8) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x6 x7 = x4 x7 x6) ⟶ prim1 x2 x0 ⟶ (x2 = x1 ⟶ ∀ x6 : ο . x6) ⟶ (∀ x6 . prim1 x6 x0 ⟶ x4 x2 x6 = x6) ⟶ (∀ x6 . prim1 x6 x0 ⟶ (x6 = x1 ⟶ ∀ x7 : ο . x7) ⟶ ∀ x7 : ο . (∀ x8 . and (prim1 x8 x0) (x4 x6 x8 = x2) ⟶ x7) ⟶ x7) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 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 : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (explicit_Field_minus x0 x1 x2 x3 x4 x5) x0
Known 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 : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 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 : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x3 (explicit_Field_minus x0 x1 x2 x3 x4 x5) x5 = x1
Known explicit_Field_minus_R : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x3 x5 (explicit_Field_minus x0 x1 x2 x3 x4 x5) = x1
Known explicit_Field_dist_R : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 (x3 x5 x6) x7 = x3 (x4 x5 x7) (x4 x6 x7)
Known explicit_Field_minus_plus_dist : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 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 : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 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 : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 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 : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x4 x1 x5 = x1
Known explicit_Field_zero_multR : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x4 x5 x1 = x1
Known explicit_Field_minus_one_In : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ prim1 (explicit_Field_minus x0 x1 x2 x3 x4 x2) x0
Theorem 2f9e6.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . explicit_Field x0 x1 x2 x3 x4 ⟶ ∀ x5 : ο . ((∀ x6 . prim1 x6 x0 ⟶ prim1 (explicit_Field_minus x0 x1 x2 x3 x4 x6) x0) ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x1 = x1 ⟶ (∀ x6 . prim1 x6 x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x6) = x6) ⟶ (∀ x6 . prim1 x6 x0 ⟶ x3 (explicit_Field_minus x0 x1 x2 x3 x4 x6) x6 = x1) ⟶ (∀ x6 . prim1 x6 x0 ⟶ x3 x6 (explicit_Field_minus x0 x1 x2 x3 x4 x6) = x1) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x4 (x3 x6 x7) x8 = x3 (x4 x6 x8) (x4 x7 x8)) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 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 . prim1 x6 x0 ⟶ ∀ x7 . prim1 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 . prim1 x6 x0 ⟶ ∀ x7 . prim1 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 . prim1 x6 x0 ⟶ x4 x1 x6 = x1) ⟶ (∀ x6 . prim1 x6 x0 ⟶ x4 x6 x1 = x1) ⟶ prim1 (explicit_Field_minus x0 x1 x2 x3 x4 x2) x0 ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ prim1 (x4 x6 (x4 x7 x8)) x0) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 (x3 x6 x7) (x3 x8 x9) = x3 (x3 x6 x9) (x3 x7 x8)) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 (x3 x6 x7) (x3 x8 x9) = x3 (x3 x6 x8) (x3 x7 x9)) ⟶ x5) ⟶ x5 (proof)
Param 62ee1.. : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Param 3b429.. : ι → (ι → ι) → (ι → ι → ο) → CT2 ι
Definition True := ∀ x0 : ο . x0 ⟶ x0
Param 1216a.. : ι → (ι → ο) → ι
Param explicit_OrderedField : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Param lt : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ι → ι → ο
Param natOfOrderedField_p : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ι → ο
Param b5c9f.. : ι → ι → ι
Param f482f.. : ι → ι → ι
Known f2fa8.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ο . (62ee1.. x0 x1 x2 x3 x4 x5 ⟶ explicit_OrderedField x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ lt x0 x1 x2 x3 x4 x5 x1 x7 ⟶ x5 x1 x8 ⟶ ∀ x9 : ο . (∀ x10 . and (prim1 x10 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5))) (x5 x8 (x4 x10 x7)) ⟶ x9) ⟶ x9) ⟶ (∀ x7 . prim1 x7 (b5c9f.. x0 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5))) ⟶ ∀ x8 . prim1 x8 (b5c9f.. x0 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5))) ⟶ (∀ x9 . prim1 x9 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ and (and (x5 (f482f.. x7 x9) (f482f.. x8 x9)) (x5 (f482f.. x7 x9) (f482f.. x7 (x3 x9 x2)))) (x5 (f482f.. x8 (x3 x9 x2)) (f482f.. x8 x9))) ⟶ ∀ x9 : ο . (∀ x10 . and (prim1 x10 x0) (∀ x11 . prim1 x11 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ and (x5 (f482f.. x7 x11) x10) (x5 x10 (f482f.. x8 x11))) ⟶ x9) ⟶ x9) ⟶ x6) ⟶ 62ee1.. x0 x1 x2 x3 x4 x5 ⟶ x6
Param iff : ο → ο → ο
Param or : ο → ο → ο
Known 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 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x5 x7 x8 ⟶ x5 x8 x9 ⟶ x5 x7 x9) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (and (x5 x7 x8) (x5 x8 x7)) (x7 = x8)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ or (x5 x7 x8) (x5 x8 x7)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x5 x7 x8 ⟶ x5 (x3 x7 x9) (x3 x8 x9)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x5 x1 x7 ⟶ x5 x1 x8 ⟶ x5 x1 (x4 x7 x8)) ⟶ x6) ⟶ explicit_OrderedField x0 x1 x2 x3 x4 x5 ⟶ x6
Known b2421.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . prim1 x2 x0 ⟶ x1 x2 ⟶ prim1 x2 (1216a.. x0 x1)
Known Eps_i_ex : ∀ x0 : ι → ο . (∀ x1 : ο . (∀ x2 . x0 x2 ⟶ x1) ⟶ x1) ⟶ x0 (prim0 x0)
Known andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Known 0cbcb.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ι → ι . ∀ x4 . prim1 x4 (3b429.. x0 x1 x2 x3) ⟶ ∀ x5 : ο . (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 (x1 x6) ⟶ x2 x6 x7 ⟶ x4 = x3 x6 x7 ⟶ x5) ⟶ x5
Known 81c0c.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ι → ι . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 (x1 x4) ⟶ x2 x4 x5 ⟶ prim1 (x3 x4 x5) (3b429.. x0 x1 x2 x3)
Known TrueI : True
Theorem 6e27d.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . 62ee1.. x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10)) ⟶ ∀ x7 : ο . ((∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim1 (x6 x8 x9) (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6)) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x8 = x6 x10 x11 ⟶ x9 (x6 x10 x11)) ⟶ x9 x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x6 x8 x9 = x6 x11 x13) ⟶ x12) ⟶ x12)) = x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim0 (λ x11 . and (prim1 x11 x0) (x6 x8 x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = x9) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ prim1 (prim0 (λ x9 . and (prim1 x9 x0) (∀ x10 : ο . (∀ x11 . and (prim1 x11 x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10))) x0) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ prim1 (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) x0) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ x8 = x6 (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) ⟶ (∀ x8 . prim1 x8 x0 ⟶ prim1 (x6 x8 x1) (1216a.. (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) (λ x9 . x6 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12))) x1 = x9))) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12)) = prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) ⟶ x8 = x9) ⟶ prim1 (x6 x1 x1) (3b429.. x0 (λ x8 . x0) (λ x8 x9 . True) x6) ⟶ prim1 (x6 x2 x1) (3b429.. x0 (λ x8 . x0) (λ x8 x9 . True) x6) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 (x3 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x10 x11 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (prim1 x13 x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x6 x8 x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x6 x10 x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x6 (x3 x8 x10) (x3 x9 x11)) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ x6 (x3 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (x3 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) = x6 (x3 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (x3 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))))) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim1 (x6 (x3 (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (x3 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))))) (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6)) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x6 (x3 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (x3 (prim0 (λ x15 . and (prim1 x15 x0) (x8 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (prim1 x15 x0) (x9 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) = x6 x11 x13) ⟶ x12) ⟶ x12)) = x3 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (x6 (x3 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (prim1 x13 x0) (x8 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 (x3 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (x3 (prim0 (λ x17 . and (prim1 x17 x0) (x8 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∀ x20 : ο . (∀ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (prim1 x17 x0) (x9 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∀ x20 : ο . (∀ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = x3 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 (x3 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x10 x11 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x6 x8 x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x6 x10 x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (prim1 x13 x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x6 x10 x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) (x4 (prim0 (λ x13 . and (prim1 x13 x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x6 x8 x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 x10 x11 = x6 x13 x15) ⟶ x14) ⟶ 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 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ x6 (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12))))) = x6 (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))))) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim1 (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))))) x0) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim1 (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11))))) x0) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim1 (x6 (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∀ x13 : ο . (∀ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (∀ x11 : ο . (∀ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))))) (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6)) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x6 (x3 (x4 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x15 . and (prim1 x15 x0) (x8 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (prim1 x15 x0) (x9 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))))) (x3 (x4 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (prim1 x15 x0) (x9 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) (x4 (prim0 (λ x15 . and (prim1 x15 x0) (x8 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))))) = x6 x11 x13) ⟶ x12) ⟶ x12)) = x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ ∀ x9 . prim1 x9 (3b429.. x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (x6 (x3 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (x8 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (prim1 x13 x0) (x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) (x4 (prim0 (λ x13 . and (prim1 x13 x0) (x8 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∀ x16 : ο . (∀ x17 . and (prim1 x17 x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))))) = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x6 (x3 (x4 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x17 . and (prim1 x17 x0) (x8 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∀ x20 : ο . (∀ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (prim1 x17 x0) (x9 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∀ x20 : ο . (∀ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))))) (x3 (x4 (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (prim1 x17 x0) (x9 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∀ x20 : ο . (∀ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) (x4 (prim0 (λ x17 . and (prim1 x17 x0) (x8 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∀ x20 : ο . (∀ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (prim1 x17 x0) (∀ x18 : ο . (∀ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∀ x14 : ο . (∀ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (∀ x12 : ο . (∀ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12))))) ⟶ x7) ⟶ x7 (proof)