| ∀ x0 : (ι → ι → ((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : (((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 → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . setsum 0 x10) 0) 0 (λ x9 x10 x11 . 0) (x1 (λ x9 . λ x10 : ι → ι . x6) (setsum (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 0) 0 (x5 0)) (setsum (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . 0)) (x5 0)))) = setsum 0 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . setsum (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . x3 (λ x16 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x16 x17 x18 . 0) 0) (λ x13 . x12 (λ x14 . 0))) (x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . x7 0 (λ x11 x12 . 0)) (Inj0 0) (λ x10 x11 x12 . 0) 0) 0) (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (setsum (x6 0) (Inj1 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . x11 0 (λ x13 . 0)) (λ x10 . x1 (λ x11 . λ x12 : ι → ι . 0) 0)))) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x10) (setsum (x7 0 (λ x12 x13 . 0)) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x12 x13 x14 . 0) 0)) (λ x12 x13 x14 . 0) x9) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) x4 (x7 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . 0)) (λ x9 x10 . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . 0) (λ x11 . 0)))) (setsum (setsum (setsum 0 0) 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x9) (setsum 0 0) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x9 x10 x11 . 0) 0)))) (λ x9 x10 x11 . 0) 0 = x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . x3 (λ x15 : ι → (ι → ι → ι) → ι → ι . x1 (λ x16 . λ x17 : ι → ι . 0) 0) 0 (λ x15 x16 x17 . x3 (λ x18 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x18 x19 x20 . 0) 0) 0) (λ x12 . x3 (λ x13 : ι → (ι → ι → ι) → ι → ι . x10) (Inj0 0) (λ x13 x14 x15 . setsum 0 0) 0))) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . setsum 0 0)) (x6 (x1 (λ x9 . λ x10 : ι → ι . 0) (Inj1 (x1 (λ x9 . λ x10 : ι → ι . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x11) (λ x9 . 0) = x4 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (x9 (λ x11 . setsum (x1 (λ x12 . λ x13 : ι → ι . 0) 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x12 . 0))) (x7 (λ x11 . λ x12 : ι → ι . λ x13 . 0)))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x1 (λ x12 . λ x13 : ι → ι . setsum (Inj1 (setsum 0 0)) (x13 (setsum 0 0))) 0) (λ x9 . 0) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . 0) (setsum (Inj0 0) (x6 (x7 0)))) 0 = Inj0 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 . λ x13 : ι → ι . 0) 0) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x12 . 0)) (λ x12 x13 x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . 0) (λ x15 . 0)) (x7 0))) x5 (x4 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . Inj1 (x7 (x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . x13) (λ x11 . 0)))) (setsum 0 (x4 0)) = x7 (Inj1 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x7 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x10 x11 x12 . 0) 0) (x1 (λ x10 . λ x11 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . Inj0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . Inj0 (x11 (λ x15 . 0))) (λ x12 . Inj0 (setsum 0 0)))) (x7 (λ x9 . x1 (λ x10 . λ x11 : ι → ι . Inj0 (setsum 0 0)) (setsum (setsum 0 0) (Inj1 0))) x5 (λ x9 . 0)) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x11 0) 0 (λ x12 x13 x14 . 0) (x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0)) x5) 0 (λ x9 x10 x11 . 0) x4) = x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . Inj0 (x9 0 (λ x11 x12 . Inj0 0) 0)) (x7 (λ x10 . x9 x10 (λ x11 x12 . setsum 0 0) (x3 (λ x11 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x11 x12 x13 . 0) 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . x9 0 (λ x13 x14 . 0) 0) (λ x10 . x10)) (λ x10 . x6)) (λ x10 x11 x12 . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . 0) (x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . x15 (λ x16 . 0)) x10 x12) x12) x6) x6 (λ x9 x10 x11 . setsum (Inj0 (setsum 0 x11)) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) (Inj0 (x7 (λ x12 . 0) 0 (λ x12 . 0))) (λ x12 x13 . x3 (λ x14 : ι → (ι → ι → ι) → ι → ι . setsum 0 0) 0 (λ x14 x15 x16 . x15)) (setsum (Inj0 0) (x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0)))) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . 0) (setsum 0 (Inj0 (x1 (λ x9 . λ x10 : ι → ι . 0) 0))) (λ x9 x10 x11 . x7 (λ x12 . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . 0) (λ x13 . x13)) 0 (λ x12 . x11)) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 (x1 (λ x12 . λ x13 : ι → ι . 0) 0)) 0 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 . λ x13 : ι → ι . Inj1 (setsum (setsum 0 0) (Inj0 0))) x9) (x4 (λ x9 x10 . x9) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (Inj1 0) x10) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0) (setsum 0 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 0)) (x1 (λ x9 . λ x10 : ι → ι . 0) (setsum 0 0))) 0) (setsum (setsum 0 0) 0) = setsum (x5 (λ x9 : (ι → ι) → ι → ι . x6)) (Inj1 (Inj0 (x4 (λ x9 x10 . Inj1 0) (Inj1 0) x6)))) ⟶ False |
|