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