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