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