Proofgold Signed Transaction

Param 62ee1.. : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Definition and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Param 3b429.. : ι → (ι → ι) → (ι → ι → ο) → CT2 ι
Param True : ο
Param 1216a.. : ι → (ι → ο) → ι
Param explicit_Field_minus : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι
Known 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 . and (prim1 x12 x0) (x6 x8 x9 = x6 x11 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 . and (prim1 x14 x0) (x6 x8 x9 = x6 x13 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 . and (prim1 x10 x0) (x8 = x6 x9 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 . and (prim1 x12 x0) (x8 = x6 x11 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 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 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 . and (prim1 x12 x0) (x9 = x6 x11 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 . and (prim1 x12 x0) (x8 = x6 x11 x12))) = prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12))) ⟶ prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11)) = prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 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 . and (prim1 x14 x0) (x6 x8 x9 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x6 x10 x11 = x6 x13 x14))))) (x3 (prim0 (λ x13 . and (prim1 x13 x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x6 x8 x9 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x6 x10 x11 = x6 x15 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 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12))))) (x3 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))) x11)))) = x6 (x3 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12))))) (x3 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 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 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 x11))))) (x3 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 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 . and (prim1 x12 x0) (x6 (x3 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x8 = x6 x15 x16)))) (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x9 = x6 x15 x16))))) (x3 (prim0 (λ x15 . and (prim1 x15 x0) (x8 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x8 = x6 x17 x18)))) x15))) (prim0 (λ x15 . and (prim1 x15 x0) (x9 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x9 = x6 x17 x18)))) x15)))) = x6 x11 x12))) = x3 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 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 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14))))) (x3 (prim0 (λ x13 . and (prim1 x13 x0) (x8 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x8 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x9 = x6 x15 x16)))) x13)))) = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x6 (x3 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x8 = x6 x17 x18)))) (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x9 = x6 x17 x18))))) (x3 (prim0 (λ x17 . and (prim1 x17 x0) (x8 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∃ x20 . and (prim1 x20 x0) (x8 = x6 x19 x20)))) x17))) (prim0 (λ x17 . and (prim1 x17 x0) (x9 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∃ x20 . and (prim1 x20 x0) (x9 = x6 x19 x20)))) x17)))) = x6 x13 x14)))) x11)) = x3 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 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 . and (prim1 x14 x0) (x6 x8 x9 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x6 x10 x11 = x6 x13 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 . and (prim1 x16 x0) (x6 x8 x9 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x6 x10 x11 = x6 x15 x16)))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x6 x8 x9 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x6 x10 x11 = x6 x15 x16)))) x13)))) (x4 (prim0 (λ x13 . and (prim1 x13 x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x6 x8 x9 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 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 . 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 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 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 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12)))))) = x6 (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 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 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 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 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 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 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 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 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) x10)))) (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 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 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 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 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) x10)))) (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 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 . and (prim1 x12 x0) (x6 (x3 (x4 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x8 = x6 x15 x16)))) (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x9 = x6 x15 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 . and (prim1 x18 x0) (x8 = x6 x17 x18)))) x15))) (prim0 (λ x15 . and (prim1 x15 x0) (x9 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x9 = x6 x17 x18)))) x15)))))) (x3 (x4 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x8 = x6 x15 x16)))) (prim0 (λ x15 . and (prim1 x15 x0) (x9 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x9 = x6 x17 x18)))) x15)))) (x4 (prim0 (λ x15 . and (prim1 x15 x0) (x8 = x6 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x8 = x6 x17 x18)))) x15))) (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x9 = x6 x15 x16)))))) = x6 x11 x12))) = x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 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 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 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 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 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 . and (prim1 x16 x0) (x8 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x9 = x6 x15 x16)))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (x9 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x9 = x6 x15 x16)))) x13)))) (x4 (prim0 (λ x13 . and (prim1 x13 x0) (x8 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x8 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))))) = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x6 (x3 (x4 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x8 = x6 x17 x18)))) (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x9 = x6 x17 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 . and (prim1 x20 x0) (x8 = x6 x19 x20)))) x17))) (prim0 (λ x17 . and (prim1 x17 x0) (x9 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∃ x20 . and (prim1 x20 x0) (x9 = x6 x19 x20)))) x17)))))) (x3 (x4 (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x8 = x6 x17 x18)))) (prim0 (λ x17 . and (prim1 x17 x0) (x9 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∃ x20 . and (prim1 x20 x0) (x9 = x6 x19 x20)))) x17)))) (x4 (prim0 (λ x17 . and (prim1 x17 x0) (x8 = x6 (prim0 (λ x19 . and (prim1 x19 x0) (∃ x20 . and (prim1 x20 x0) (x8 = x6 x19 x20)))) x17))) (prim0 (λ x17 . and (prim1 x17 x0) (∃ x18 . and (prim1 x18 x0) (x9 = x6 x17 x18)))))) = x6 x13 x14)))) x11)) = x3 (x4 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) (prim0 (λ x11 . and (prim1 x11 x0) (x9 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x9 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (prim1 x11 x0) (x8 = x6 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x8 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12)))))) ⟶ x7) ⟶ x7
Theorem 1a4bb.. : ∀ 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 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ 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 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x6 x8 x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x6 x8 x9 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = x9) ⟶ (∀ x8 . prim1 x8 (3b429.. x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ prim1 (prim0 (λ x9 . ∀ x10 : ο . (prim1 x9 x0 ⟶ (∃ 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 . ∀ x10 : ο . (prim1 x9 x0 ⟶ x8 = x6 (prim0 (λ x12 . ∀ x13 : ο . (prim1 x12 x0 ⟶ (∃ x14 . and (prim1 x14 x0) (x8 = x6 x12 x14)) ⟶ x13) ⟶ x13)) x9 ⟶ x10) ⟶ 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) ⟶ prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13)) ⟶ x12) ⟶ x12) = prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13)) ⟶ x12) ⟶ x12) ⟶ prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) ⟶ 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 (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 . ∀ x11 : ο . (prim1 x10 x0 ⟶ (∃ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12)) ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ (∃ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12)) ⟶ x11) ⟶ x11))) (x3 (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (prim1 x13 x0 ⟶ (∃ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15)) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (prim1 x13 x0 ⟶ (∃ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15)) ⟶ x14) ⟶ x14)) x10 ⟶ 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 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x6 (x3 (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ (∃ x18 . and (prim1 x18 x0) (x8 = x6 x16 x18)) ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ (∃ x18 . and (prim1 x18 x0) (x9 = x6 x16 x18)) ⟶ x17) ⟶ x17))) (x3 (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21)) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21)) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17))) = x6 x11 x13)) ⟶ x12) ⟶ x12) = x3 (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13)) ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ 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 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x6 (x3 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15))) (x3 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (prim1 x17 x0 ⟶ (∃ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19)) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (prim1 x17 x0 ⟶ (∃ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19)) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15))) = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x6 (x3 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21)) ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21)) ⟶ x20) ⟶ x20))) (x3 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (prim1 x22 x0 ⟶ (∃ x24 . and (prim1 x24 x0) (x8 = x6 x22 x24)) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (prim1 x22 x0 ⟶ (∃ x24 . and (prim1 x24 x0) (x9 = x6 x22 x24)) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20))) = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = x3 (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ 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 (x6 (x3 (x4 (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ (∃ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12)) ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ (∃ x12 . and (prim1 x12 x0) (x9 = x6 x10 x12)) ⟶ x11) ⟶ x11))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (prim1 x13 x0 ⟶ (∃ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15)) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (prim1 x13 x0 ⟶ (∃ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15)) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11))))) (x3 (x4 (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ (∃ x12 . and (prim1 x12 x0) (x8 = x6 x10 x12)) ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (prim1 x13 x0 ⟶ (∃ x15 . and (prim1 x15 x0) (x9 = x6 x13 x15)) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11))) (x4 (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (prim1 x13 x0 ⟶ (∃ x15 . and (prim1 x15 x0) (x8 = x6 x13 x15)) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (prim1 x10 x0 ⟶ (∃ 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 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x6 (x3 (x4 (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ (∃ x18 . and (prim1 x18 x0) (x8 = x6 x16 x18)) ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ (∃ x18 . and (prim1 x18 x0) (x9 = x6 x16 x18)) ⟶ x17) ⟶ x17))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21)) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21)) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17))))) (x3 (x4 (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ (∃ x18 . and (prim1 x18 x0) (x8 = x6 x16 x18)) ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21)) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17))) (x4 (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21)) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (prim1 x16 x0 ⟶ (∃ x18 . and (prim1 x18 x0) (x9 = x6 x16 x18)) ⟶ x17) ⟶ x17)))) = x6 x11 x13)) ⟶ x12) ⟶ x12) = x3 (x4 (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13)) ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13)) ⟶ x12) ⟶ x12))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ 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 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x6 (x3 (x4 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (prim1 x17 x0 ⟶ (∃ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19)) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (prim1 x17 x0 ⟶ (∃ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19)) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15))))) (x3 (x4 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (prim1 x17 x0 ⟶ (∃ x19 . and (prim1 x19 x0) (x9 = x6 x17 x19)) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15))) (x4 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (prim1 x17 x0 ⟶ (∃ x19 . and (prim1 x19 x0) (x8 = x6 x17 x19)) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15)))) = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x6 (x3 (x4 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21)) ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21)) ⟶ x20) ⟶ x20))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (prim1 x22 x0 ⟶ (∃ x24 . and (prim1 x24 x0) (x8 = x6 x22 x24)) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (prim1 x22 x0 ⟶ (∃ x24 . and (prim1 x24 x0) (x9 = x6 x22 x24)) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20))))) (x3 (x4 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x8 = x6 x19 x21)) ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (prim1 x22 x0 ⟶ (∃ x24 . and (prim1 x24 x0) (x9 = x6 x22 x24)) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20))) (x4 (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (prim1 x22 x0 ⟶ (∃ x24 . and (prim1 x24 x0) (x8 = x6 x22 x24)) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (prim1 x19 x0 ⟶ (∃ x21 . and (prim1 x21 x0) (x9 = x6 x19 x21)) ⟶ x20) ⟶ x20)))) = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = x3 (x4 (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x8 = x6 x11 x13)) ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x9 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12))) (x4 (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (prim1 x14 x0 ⟶ (∃ x16 . and (prim1 x16 x0) (x8 = x6 x14 x16)) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (prim1 x11 x0 ⟶ (∃ x13 . and (prim1 x13 x0) (x9 = x6 x11 x13)) ⟶ x12) ⟶ x12)))) ⟶ x7) ⟶ x7
Param explicit_Field : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param 11fac.. : ι → (ι → ι) → (ι → ι) → ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param Subq : ι → ι → ο
Known 424a2.. : ∀ 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)) ⟶ explicit_Field (3b429.. x0 (λ x7 . x0) (λ x7 x8 . True) x6) (x6 x1 x1) (x6 x2 x1) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))) (x3 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9)))) (x4 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))))) ⟶ and (11fac.. (3b429.. x0 (λ x7 . x0) (λ x7 x8 . True) x6) (λ x7 . x6 (prim0 (λ x8 . and (prim1 x8 x0) (∃ x9 . and (prim1 x9 x0) (x7 = x6 x8 x9)))) x1) (λ x7 . x6 (prim0 (λ x8 . and (prim1 x8 x0) (x7 = x6 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x7 = x6 x10 x11)))) x8))) x1) (x6 x1 x1) (x6 x2 x1) (x6 x1 x2) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))) (x3 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9)))) (x4 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10)))))))) ((∀ x7 . prim1 x7 x0 ⟶ x6 x7 x1 = x7) ⟶ and (and (and (and (and (Subq x0 (3b429.. x0 (λ x7 . x0) (λ x7 x8 . True) x6)) (∀ x7 . prim1 x7 x0 ⟶ prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10))) = x7)) (x6 x1 x1 = x1)) (x6 x2 x1 = x2)) (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x6 (x3 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x7 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11))))) (x3 (prim0 (λ x10 . and (prim1 x10 x0) (x7 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x7 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10)))) = x3 x7 x8)) (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x6 (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x7 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x7 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x7 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x7 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10)))) (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x7 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x7 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))))) = x4 x7 x8))
Theorem 079d2.. : ∀ 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)) ⟶ explicit_Field (3b429.. x0 (λ x7 . x0) (λ x7 x8 . True) x6) (x6 x1 x1) (x6 x2 x1) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))) (x3 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x8 = x6 x11 x12)))) x9)))) (x4 (prim0 (λ x9 . and (prim1 x9 x0) (x7 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10))))))) ⟶ ∀ x7 : ο . (11fac.. (3b429.. x0 (λ x8 . x0) (λ x8 x9 . True) x6) (λ x8 . x6 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10)))) x1) (λ x8 . x6 (prim0 (λ x9 . and (prim1 x9 x0) (x8 = x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 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 (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 x11))))) (x3 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) x10))))) (λ x8 x9 . x6 (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 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 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) (prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) x10)))) (x4 (prim0 (λ x10 . and (prim1 x10 x0) (x8 = x6 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x8 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 x11))))))) ⟶ ((∀ x8 . prim1 x8 x0 ⟶ x6 x8 x1 = x8) ⟶ ∀ x8 : ο . ((∀ x9 : ο . ((∀ x10 : ο . ((∀ x11 : ο . ((∀ x12 : ο . (Subq x0 (3b429.. x0 (λ x13 . x0) (λ x13 x14 . True) x6) ⟶ (∀ x13 . prim1 x13 x0 ⟶ prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x13 = x6 x15 x16))) = x13) ⟶ x12) ⟶ x12) ⟶ x6 x1 x1 = x1 ⟶ x11) ⟶ x11) ⟶ x6 x2 x1 = x2 ⟶ x10) ⟶ x10) ⟶ (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 (x3 (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x10 = x6 x13 x14)))) (prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x11 = x6 x13 x14))))) (x3 (prim0 (λ x13 . and (prim1 x13 x0) (x10 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x10 = x6 x15 x16)))) x13))) (prim0 (λ x13 . and (prim1 x13 x0) (x11 = x6 (prim0 (λ x15 . and (prim1 x15 x0) (∃ x16 . and (prim1 x16 x0) (x11 = x6 x15 x16)))) x13)))) = x3 x10 x11) ⟶ x9) ⟶ x9) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x6 (x3 (x4 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x10 = x6 x12 x13))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x12 . and (prim1 x12 x0) (x9 = x6 (prim0 (λ x14 . and (prim1 x14 x0) (∃ x15 . and (prim1 x15 x0) (x9 = x6 x14 x15)))) x12))) (prim0 (λ x12 . and (prim1 x12 x0) (x10 = x6 (prim0 (λ x14 . and (prim1 x14 x0) (∃ x15 . and (prim1 x15 x0) (x10 = x6 x14 x15)))) x12)))))) (x3 (x4 (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x9 = x6 x12 x13)))) (prim0 (λ x12 . and (prim1 x12 x0) (x10 = x6 (prim0 (λ x14 . and (prim1 x14 x0) (∃ x15 . and (prim1 x15 x0) (x10 = x6 x14 x15)))) x12)))) (x4 (prim0 (λ x12 . and (prim1 x12 x0) (x9 = x6 (prim0 (λ x14 . and (prim1 x14 x0) (∃ x15 . and (prim1 x15 x0) (x9 = x6 x14 x15)))) x12))) (prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x10 = x6 x12 x13)))))) = x4 x9 x10) ⟶ x8) ⟶ x8) ⟶ x7) ⟶ x7