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