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