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