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