| ∀ x0 : (ι → (ι → (ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x1 : (ι → ι) → (ι → ι → ι → ι) → ι → ι → ι . ∀ x2 : (ι → ι) → ι → ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → (ι → ((ι → ι) → ι) → ι) → ι . (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . Inj0 (Inj0 (x1 (λ x10 . setsum 0 0) (λ x10 x11 x12 . Inj1 0) x7 0))) (λ x9 . λ x10 : (ι → ι) → ι . 0) = x4 (λ x9 . λ x10 : ι → ι . λ x11 . x11) x7 (λ x9 . x2 (λ x10 . x3 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0)) (x2 (λ x10 . x6) x7 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x12) (λ x10 . 0)) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x0 (λ x13 . λ x14 : ι → (ι → ι) → ι . setsum x12 x13) (λ x13 . setsum (Inj0 0) (x1 (λ x14 . 0) (λ x14 x15 x16 . 0) 0 0))) (λ x10 . x2 (λ x11 . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι . 0) (λ x12 . x3 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0))) x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . x12 0) (x11 0 0) (λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . x1 (λ x17 . 0) (λ x17 x18 x19 . 0) 0 0) (λ x14 . 0)) (λ x11 . x11))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x5) (λ x9 . λ x10 : (ι → ι) → ι . 0) = x5) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι) → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 . x7 (x7 (Inj1 (setsum 0 0)))) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x11) (λ x9 . x1 (λ x10 . 0) (λ x10 x11 x12 . Inj0 (setsum (x0 (λ x13 . λ x14 : ι → (ι → ι) → ι . 0) (λ x13 . 0)) 0)) (setsum (Inj0 (x3 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0))) x9) (Inj1 (x3 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0)))) = x1 (λ x9 . x7 0) (λ x9 x10 x11 . x7 0) (Inj0 (x2 (λ x9 . setsum 0 (Inj1 0)) (setsum (setsum 0 0) (Inj0 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 . x12) (λ x12 . λ x13 : (ι → ι) → ι . Inj0 0)) (λ x9 . x9))) (setsum (x3 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (setsum 0 0))) (setsum (Inj1 (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι . 0) (λ x9 . 0))) 0))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 . x6) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 . x9 (Inj0 x12) x12) (x1 (λ x12 . 0) (λ x12 x13 x14 . Inj1 (x3 (λ x15 . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0))) 0 (setsum 0 (setsum 0 0))) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) (x1 (λ x12 . Inj1 x11) (λ x12 x13 x14 . 0) (setsum 0 (x2 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) (λ x12 . 0))))) (λ x9 . 0) = Inj1 0) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . 0) (λ x9 x10 x11 . 0) x5 0 = x5) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 . setsum (x2 (λ x10 . 0) (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι . setsum 0 0) (λ x10 . setsum 0 0)) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x0 (λ x13 . λ x14 : ι → (ι → ι) → ι . setsum 0 0) (λ x13 . x11 0)) (λ x10 . Inj1 (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι . 0) (λ x11 . 0)))) 0) (λ x9 x10 x11 . x7 (λ x12 . x11)) (x1 (λ x9 . x7 (λ x10 . 0)) (λ x9 x10 x11 . x10) (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι . x3 (λ x11 . x9) (λ x11 . λ x12 : (ι → ι) → ι . setsum 0 0)) (λ x9 . x2 (λ x10 . 0) (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι . 0) (λ x10 . 0)) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj0 0) (λ x10 . Inj1 0))) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x10 (setsum 0 0)) (x5 0 (λ x9 : ι → ι . 0)))) (x2 (λ x9 . x7 (λ x10 . 0)) (x5 0 (λ x9 : ι → ι . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . Inj0 (x2 (λ x12 . setsum 0 0) 0 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . Inj0 0) (λ x12 . x12))) (λ x9 . setsum 0 0)) = Inj1 (x3 (λ x9 . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum (x7 (λ x11 . Inj1 0)) (x10 (λ x11 . x9))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι . x1 (λ x11 . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι . setsum (Inj0 0) (x2 (λ x14 . 0) 0 (λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . 0) (λ x14 . 0))) (λ x12 . x10 (x1 (λ x13 . 0) (λ x13 x14 x15 . 0) 0 0) (λ x13 . 0))) (λ x11 x12 x13 . setsum (x0 (λ x14 . λ x15 : ι → (ι → ι) → ι . x14) (λ x14 . Inj0 0)) (x2 (λ x14 . Inj1 0) (setsum 0 0) (λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . x15 0) (λ x14 . 0))) x6 (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι . 0) (λ x11 . Inj0 (x10 0 (λ x12 . 0))))) (λ x9 . setsum (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι . 0) (λ x10 . 0)) 0) = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι . x2 (λ x11 . x1 (λ x12 . x11) (λ x12 x13 x14 . 0) (Inj1 (setsum 0 0)) (Inj1 0)) (x10 x7 (λ x11 . 0)) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 . λ x15 : ι → (ι → ι) → ι . 0) (λ x14 . 0)) (λ x11 . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι . 0) (λ x12 . Inj1 0))) (λ x9 . 0) = x2 (λ x9 . x2 (λ x10 . x7) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . x1 (λ x12 . Inj1 0) (λ x12 x13 x14 . setsum 0 (x3 (λ x15 . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0))) (x10 (Inj0 0) (Inj0 0))) (λ x10 . setsum (x1 (λ x11 . 0) (λ x11 x12 x13 . x11) (x2 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x11 . 0)) 0) (x1 (λ x11 . 0) (λ x11 x12 x13 . x13) (setsum 0 0) x7))) (setsum (setsum (x2 (λ x9 . Inj0 0) (x2 (λ x9 . 0) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x9 . x3 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0))) (x3 (λ x9 . setsum 0 0) (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 . 0) (λ x11 x12 x13 . 0) 0 0))) 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x11) (λ x9 . x1 (λ x10 . x1 (λ x11 . x1 (λ x12 . 0) (λ x12 x13 x14 . 0) (x2 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) (λ x12 . 0)) 0) (λ x11 x12 x13 . 0) x7 (Inj1 (setsum 0 0))) (λ x10 x11 x12 . 0) x6 (setsum (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι . Inj1 0) (λ x10 . 0)) 0))) ⟶ False |
|