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