Proofgold Signed Transaction

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
Known 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
Param 62ee1.. : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Param and : ο → ο → ο
Param 3b429.. : ι → (ι → ι) → (ι → ι → ο) → CT2 ι
Param True : ο
Param 1216a.. : ι → (ι → ο) → 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
Known b6a82.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . ∀ x7 . (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x8 x9 = x6 x10 x11 ⟶ and (x8 = x10) (x9 = x11)) ⟶ 62ee1.. x0 x1 x2 x3 x4 x5 ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x8 x9 = x3 x9 x8) ⟶ prim1 x1 x0 ⟶ (∀ x8 . prim1 x8 x0 ⟶ x3 x1 x8 = x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim1 (x4 x8 x9) x0) ⟶ (∀ 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 ⟶ prim1 (x6 x8 x1) (1216a.. x7 (λ x9 . x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12)))) x1 = x9))) ⟶ (∀ x8 . prim1 x8 x7 ⟶ prim1 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10)))) x0) ⟶ (∀ 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 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))) ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x1 = x1 ⟶ (∀ x8 . prim1 x8 x0 ⟶ x4 x1 x8 = x1) ⟶ (∀ x8 . prim1 x8 x0 ⟶ x4 x8 x1 = x1) ⟶ 62ee1.. (1216a.. x7 (λ x8 . x6 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) x1 = x8)) (x6 x1 x1) (x6 x2 x1) (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))))))) (λ x8 x9 . x5 (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)))))
Param 11fac.. : ι → (ι → ι) → (ι → ι) → ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param Subq : ι → ι → ο
Known 65b0c.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . ∀ x7 . (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x8 x9 = x6 x10 x11 ⟶ and (x8 = x10) (x9 = x11)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim1 (x3 x8 x9) x0) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x8 x9 = x3 x9 x8) ⟶ prim1 x1 x0 ⟶ (∀ x8 . prim1 x8 x0 ⟶ x3 x1 x8 = x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim1 (x4 x8 x9) x0) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x4 x9 x8) ⟶ prim1 x2 x0 ⟶ (∀ x8 . prim1 x8 x0 ⟶ x4 x2 x8 = x8) ⟶ prim1 (explicit_Field_minus x0 x1 x2 x3 x4 x2) x0 ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ prim1 (x6 x8 x9) x7) ⟶ (∀ x8 . prim1 x8 x7 ⟶ ∀ 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 x0 ⟶ prim1 (x6 x8 x1) (1216a.. x7 (λ x9 . x6 (prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x9 = x6 x11 x12)))) x1 = x9))) ⟶ (∀ x8 . prim1 x8 x7 ⟶ prim1 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x8 = x6 x9 x10)))) x0) ⟶ (∀ x8 . prim1 x8 x7 ⟶ 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 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 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 x0 ⟶ x3 (explicit_Field_minus x0 x1 x2 x3 x4 x8) x8 = x1) ⟶ (∀ x8 . prim1 x8 x0 ⟶ x3 x8 (explicit_Field_minus x0 x1 x2 x3 x4 x8) = x1) ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x1 = x1 ⟶ (∀ x8 . prim1 x8 x0 ⟶ x4 x1 x8 = x1) ⟶ (∀ x8 . prim1 x8 x0 ⟶ x4 x8 x1 = x1) ⟶ explicit_Field x7 (x6 x1 x1) (x6 x2 x1) (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))))))) ⟶ 62ee1.. (1216a.. x7 (λ x8 . x6 (prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11)))) x1 = x8)) (x6 x1 x1) (x6 x2 x1) (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))))))) (λ x8 x9 . x5 (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))))) ⟶ and (11fac.. x7 (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) ⟶ and (and (and (and (and (Subq x0 x7) (∀ x8 . prim1 x8 x0 ⟶ prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x8 = x6 x10 x11))) = x8)) (x6 x1 x1 = x1)) (x6 x2 x1 = x2)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ 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)))) = x3 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ 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)))))) = x4 x8 x9))
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 . and (prim1 x9 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5))) (x5 x8 (x4 x9 x7))) ⟶ (∀ 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 . and (prim1 x9 x0) (∀ x11 . prim1 x11 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ and (x5 (f482f.. x7 x11) x9) (x5 x9 (f482f.. x8 x11)))) ⟶ 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 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 . and (prim1 x7 x0) (x3 x6 x7 = x1)) ⟶ (∀ 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 . and (prim1 x7 x0) (x4 x6 x7 = x2)) ⟶ (∀ 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
Theorem b4fdd.. : ∀ 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)) ⟶ 62ee1.. (1216a.. (3b429.. x0 (λ x7 . x0) (λ x7 x8 . True) x6) (λ x7 . x6 (prim0 (λ x9 . and (prim1 x9 x0) (∃ x10 . and (prim1 x10 x0) (x7 = x6 x9 x10)))) x1 = x7)) (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))))))) (λ x7 x8 . x5 (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)))))
Theorem 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))