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