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