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