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