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