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