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