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