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