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