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