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