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