| ∀ x0 : (ι → ι) → ι → ι → ι → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι) → ι . ∀ x2 : (((ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → ι) → ι → ι . ∀ x3 : ((ι → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . 0) 0 (setsum (setsum (x0 (λ x9 . 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0)) (setsum 0 0) (x0 (λ x9 . 0) 0 0 0 0) (Inj1 0)) (Inj1 (x0 (λ x9 . 0) 0 0 0 0))) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . x11))) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x11 . 0) (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . Inj0 0) (x9 0)) (setsum (setsum 0 0) 0) (setsum 0 (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0))) (x3 (λ x10 : ι → ι . 0) (Inj1 (x5 0 (λ x10 : ι → ι . 0))) 0)) (setsum (Inj0 (x0 (λ x9 . 0) x4 0 (x3 (λ x9 : ι → ι . 0) 0 0) x4)) 0) (Inj1 (x3 (λ x9 : ι → ι . 0) (x5 0 (λ x9 : ι → ι . x5 0 (λ x10 : ι → ι . 0))) 0)) = setsum (x6 0 x4) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . Inj0 0) 0 = x7 (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x9 (λ x11 . x7 (λ x12 : (ι → ι) → ι . 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x6) (x4 (x7 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x0 (λ x14 . 0) 0 0 0 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . 0)))) = x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . setsum (setsum (setsum 0 (x0 (λ x13 . 0) 0 0 0 0)) (x0 (λ x13 . x3 (λ x14 : ι → ι . 0) 0 0) x10 (x2 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) (Inj1 0) (x3 (λ x13 : ι → ι . 0) 0 0))) (Inj1 (Inj1 0))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . x10) = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . Inj1 (x0 (λ x12 . Inj0 x11) (x2 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x2 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) 0) (x2 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x14 x15 x16 . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 x15 . 0)) x7) x7 (x9 (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x15 x16 x17 . 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x15 x16 . 0)) (setsum 0 0) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 x15 . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 . 0))))) = Inj1 (x3 (λ x9 : ι → ι . 0) 0 (setsum (setsum (x5 (λ x9 . 0)) 0) (x5 (λ x9 . x3 (λ x10 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι . x0 (λ x9 . 0) 0 (x0 (λ x9 . x9) (setsum (x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x10 . 0) 0 0 0 0) x5) 0) (x7 (λ x9 x10 . x7 (λ x11 x12 . x12))) (x3 (λ x9 : ι → ι . x5) x5 0) 0) x4 (setsum x6 (x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x3 (λ x10 : ι → ι . x3 (λ x11 : ι → ι . 0) 0 0) (Inj1 0) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . 0))) (Inj0 x5))) = x0 (λ x9 . Inj1 (Inj0 (Inj1 (setsum 0 0)))) (Inj1 x6) (x0 (λ x9 . 0) 0 0 0 (x0 (λ x9 . x0 (λ x10 . 0) (x7 (λ x10 x11 . 0)) (x7 (λ x10 x11 . 0)) (x0 (λ x10 . 0) 0 0 0 0) (Inj1 0)) 0 x4 x6 x4)) x6 (Inj0 x6)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x11) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . Inj0 (x10 (λ x13 : ι → ι . λ x14 . Inj0 0) x9 0))) 0 (setsum (x3 (λ x9 : ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) (Inj1 0)) (x6 (x0 (λ x9 . 0) 0 0 0 0) (λ x9 . x7 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0)) (x3 (λ x9 : ι → ι . 0) 0 0) (setsum 0 0)) x4) (Inj1 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0)))) 0 (Inj1 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . x9 (λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0) 0 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0))) = Inj1 0) ⟶ False |
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