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