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