| ∀ x0 : (((((ι → ι) → ι → ι) → ι → ι) → 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 . ∀ x2 : (ι → ι → ι) → (((ι → ι → ι) → (ι → ι) → ι → ι) → ι) → (ι → ι) → ι → (ι → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι → ι → ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . λ x10 x11 x12 . x3 (λ x13 . x3 (λ x14 . setsum x13 (setsum 0 0)) (λ x14 : ι → ι . λ x15 x16 x17 . x14 x15)) (λ x13 : ι → ι . λ x14 x15 x16 . x16)) = x3 (λ x9 . x6) (λ x9 : ι → ι . λ x10 x11 x12 . x12)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x3 (λ x9 . x2 (λ x10 x11 . x2 (λ x12 x13 . setsum 0 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (setsum (setsum 0 0)) (setsum (Inj1 0) x11) (λ x12 . Inj1 x10)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 . 0) (x6 (Inj1 0) 0 (x5 0 (λ x10 . setsum 0 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))) (setsum 0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x12) (x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) (x6 0 0 0 0) (λ x11 . λ x12 : ι → ι . Inj1 0)) (λ x11 . λ x12 : ι → ι . x10))) (λ x9 : ι → ι . λ x10 x11 x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) x11 (λ x13 . λ x14 : ι → ι . x14 0)) = Inj1 (setsum (x6 (Inj0 (Inj1 0)) 0 0 x7) x7)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x9 x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . x2 (λ x12 x13 . x1 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . Inj1 0) 0 (λ x14 . λ x15 : ι → ι . 0)) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . x11 (λ x13 : (ι → ι) → ι → ι . λ x14 . setsum 0 0)) (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) (setsum 0 0) (λ x13 . λ x14 : ι → ι . x12)) 0 (λ x12 . Inj0 0)) (λ x11 . x7 (x7 0 (λ x12 : ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x14 . 0) 0) (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x13 . λ x14 : ι → ι . 0))) (λ x12 : ι → ι . setsum x10) (λ x12 . 0)) 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x6) (λ x10 . 0) (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 x14 x15 . 0))) (x3 (λ x10 . x6) (λ x10 : ι → ι . λ x11 x12 x13 . Inj0 0)))) (λ x9 . setsum (setsum (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)) (setsum 0 0)) (Inj1 0)) (setsum x6 0)) 0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) = setsum (setsum 0 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . x0 (λ x13 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x13 . x11) 0) (x2 (λ x9 x10 . setsum 0 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x9 . Inj1 0) 0 (λ x9 . Inj1 0)) (λ x9 . λ x10 : ι → ι . x7 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) (λ x11 : ι → ι . λ x12 . x10 0) (λ x11 . 0)))) (x3 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x10 . x9) (Inj0 0)) (λ x9 : ι → ι . λ x10 x11 x12 . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . x2 (λ x9 x10 . Inj0 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (λ x9 . setsum (Inj0 (Inj0 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)))) x6) (x2 (λ x9 x10 . setsum (x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x11 . x2 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0) 0 (λ x12 . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0))) (setsum (setsum 0 0) (setsum 0 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 . 0) 0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x2 (λ x14 x15 . x12) (λ x14 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x14 . setsum 0 0) x11 (λ x14 . x3 (λ x15 . 0) (λ x15 : ι → ι . λ x16 x17 x18 . 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . 0) (x7 (λ x10 . λ x11 : ι → ι . 0) 0 0 0)) (λ x10 . λ x11 : ι → ι . setsum (x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) x9))) (λ x9 . x5 (Inj0 (x2 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x7 (λ x11 . λ x12 : ι → ι . 0) 0 0 0) (λ x10 . setsum 0 0) (setsum 0 0) (λ x10 . x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)))) (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x10 (λ x14 : (ι → ι) → ι → ι . 0) 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . λ x13 : ι → ι . 0) 0 0 0)) (setsum x6 (x7 (λ x10 . λ x11 : ι → ι . 0) 0 0 0))) 0 (x5 (setsum x9 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x11) (Inj0 0) (λ x10 . λ x11 : ι → ι . x11 0)) 0 0)) = x2 (λ x9 x10 . Inj0 (x7 (λ x11 . λ x12 : ι → ι . x12 x11) (x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0) 0 (setsum x10 x9))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x7 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . x10) (λ x12 : ι → ι . λ x13 x14 x15 . 0)) 0 (x7 (λ x10 . λ x11 : ι → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) x10 (λ x12 . λ x13 : ι → ι . x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0))) (Inj0 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))) (Inj0 0) 0) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0))) (λ x10 . 0) (Inj1 (Inj0 0)))) (λ x9 . x2 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 . 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) (x5 0 0 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (setsum 0 0)) (λ x10 . λ x11 : ι → ι . setsum 0 (Inj0 0))) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x12) 0 (λ x11 . λ x12 : ι → ι . x3 (λ x13 . x12 0) (λ x13 : ι → ι . λ x14 x15 x16 . 0)))) x6 (λ x9 . Inj1 (setsum x6 (Inj1 (Inj0 0))))) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x3 (λ x13 . setsum x13 (x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0))) (λ x13 : ι → ι . λ x14 x15 x16 . x1 (λ x17 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x18 x19 . λ x20 : ι → ι . setsum 0 0) (setsum 0 0) (λ x17 . λ x18 : ι → ι . x3 (λ x19 . 0) (λ x19 : ι → ι . λ x20 x21 x22 . 0))))) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x9 . setsum (x5 (λ x10 : (ι → ι) → ι . λ x11 . Inj0 0)) (x2 (λ x10 x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)) (λ x10 . x9) 0 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x12 0)) 0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x11) (λ x11 : ι → ι . λ x12 x13 x14 . Inj1 0)))) (λ x9 . λ x10 : ι → ι . 0) = x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x14 . x3 (λ x15 . x1 (λ x16 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x17 x18 . λ x19 : ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . 0)) (λ x15 : ι → ι . λ x16 x17 x18 . setsum 0 0)) 0) (x2 (λ x10 x11 . setsum (x2 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0) 0 (λ x12 . 0)) (Inj1 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x10 (λ x11 x12 . 0) (λ x11 . x11) 0) (λ x10 . x3 (λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (x7 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0))) (λ x10 . 0)) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . x10))) (λ x9 . x6 (x7 (λ x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 0) (λ x11 . Inj1 0) (x6 0)))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . setsum (x9 (λ x13 : (ι → ι) → ι → ι . x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . x2 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x18 . 0) 0 (λ x18 . 0))) x10) 0) 0 (λ x9 . λ x10 : ι → ι . 0) = x4 (λ x9 : ι → ι → ι . x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . setsum 0 0) 0 (λ x13 . λ x14 : ι → ι . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x5 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . setsum (setsum 0 0) (x2 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 . 0) 0 (λ x13 . 0))))) (λ x9 . Inj1 0) (x5 (λ x9 . x2 (λ x10 x11 . x9) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x10 (λ x11 x12 . Inj1 0) (λ x11 . x10 (λ x12 x13 . 0) (λ x12 . 0) 0) (Inj0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x1 (λ x15 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x16 x17 . λ x18 : ι → ι . 0) 0 (λ x15 . λ x16 : ι → ι . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (λ x11 . λ x12 : ι → ι . Inj1 0)) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) 0) (λ x10 . setsum (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (x7 0 0)))) = setsum (setsum (x2 (λ x9 x10 . x7 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) (x7 0 0)) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 (Inj1 0)) (λ x9 . 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x13 . λ x14 : ι → ι . 0)) (x7 0 0) (λ x9 . λ x10 : ι → ι . setsum 0 0)) (λ x9 . 0)) 0) (Inj1 (x5 (λ x9 . 0)))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 x6) (λ x9 . 0) (setsum 0 (x7 (x3 (λ x9 . setsum 0 0) (λ x9 : ι → ι . λ x10 x11 x12 . Inj1 0)) (λ x9 : ι → ι . 0) 0)) = Inj0 0) ⟶ False |
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