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