| ∀ x0 : (ι → (((ι → ι) → ι → ι) → ι) → 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 → (ι → ι → ι) → ι → ι → ι) → ι → ι . ∀ x3 : (ι → ι → ι → ι) → ((((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x6 x7 . x3 (λ x9 x10 x11 . 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . setsum 0 (setsum (x2 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . Inj1 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . Inj1 0) (setsum 0 0)) (setsum (setsum 0 0) (x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) 0)))) = x7) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 x10 x11 . 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . x1 (λ x11 x12 . λ x13 : ι → ι → ι . setsum 0 (Inj0 (x13 0 0))) (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . x3 (λ x13 x14 x15 . Inj1 0) (λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι → ι . x13 (λ x15 : ι → ι . 0) (λ x15 . 0) 0)) (Inj1 (setsum 0 0)) (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x13 : ι → ι . λ x14 . 0)) (x2 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . 0) 0) (setsum 0 0) (λ x11 : ι → ι . λ x12 . 0)) (λ x11 : ι → ι . λ x12 . setsum 0 0))) = Inj0 (Inj0 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . x0 (λ x15 . λ x16 : ((ι → ι) → ι → ι) → ι . setsum (setsum 0 0) (x0 (λ x17 . λ x18 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x17 : ι → ι . λ x18 . 0))) 0 (x14 (λ x15 : ι → ι . λ x16 . x16)) (λ x15 : ι → ι . λ x16 . 0)) (x1 (λ x13 x14 . λ x15 : ι → ι → ι . setsum 0 (x3 (λ x16 x17 x18 . 0) (λ x16 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x17 : ι → ι → ι . 0))) x11) (x10 (x2 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 x16 . x15) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . x1 (λ x17 x18 . λ x19 : ι → ι → ι . 0) 0) (setsum 0 0)) (λ x13 . 0) x11) (λ x13 : ι → ι . λ x14 . x3 (λ x15 x16 x17 . x15) (λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : ι → ι → ι . 0))) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0) x7 = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . x2 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 x18 . x2 (λ x19 . λ x20 : ι → (ι → ι) → ι → ι . λ x21 x22 . x19) (λ x19 . λ x20 : ι → ι → ι . λ x21 x22 . x0 (λ x23 . λ x24 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x23 : ι → ι . λ x24 . 0)) 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . setsum 0 0) x13) (Inj1 0) x11 (λ x13 : ι → ι . λ x14 . setsum x14 (setsum 0 (x13 0)))) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 x9) (x3 (λ x9 x10 x11 . x3 (λ x12 x13 x14 . x1 (λ x15 x16 . λ x17 : ι → ι → ι . x15) (setsum 0 0)) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . x13 (x0 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0)) (x13 0 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . x3 (λ x11 x12 x13 . Inj0 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . x11 (λ x13 : ι → ι . setsum 0 0) (λ x13 . x13) 0))) = Inj0 (setsum 0 0)) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . λ x11 : ι → ι → ι . 0) (setsum (setsum x7 (x3 (λ x9 x10 x11 . x0 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . setsum 0 0))) 0) = setsum (x4 (λ x9 x10 . x7)) (x3 (λ x9 x10 x11 . 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . setsum (x9 (λ x11 : ι → ι . x0 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x11 . x1 (λ x12 x13 . λ x14 : ι → ι → ι . 0) 0) (setsum 0 0)) (setsum (x10 0 0) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι → ι . x2 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 . Inj0 (Inj1 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0) (Inj1 0)) 0 = x2 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 . x12) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . x1 (λ x15 x16 . λ x17 : ι → ι → ι . 0) (x2 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 x18 . 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . 0) 0)) (Inj0 (x2 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 x16 . setsum 0 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . x16) (setsum 0 0))) (Inj0 0) (λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . λ x17 : ι → ι → ι . Inj1 (x3 (λ x18 x19 x20 . 0) (λ x18 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x19 : ι → ι → ι . 0))) (setsum 0 (x2 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 x18 . 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . 0) 0)))) (Inj1 (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . x9) (setsum (Inj0 0) (x5 0 0)) (Inj1 (x1 (λ x9 x10 . λ x11 : ι → ι → ι . 0) 0)) (λ x9 : ι → ι . λ x10 . setsum (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0)) (x6 (λ x11 . 0)))))) ⟶ (∀ x4 : (ι → ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . Inj1 (x2 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . x2 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 x18 . setsum 0 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . setsum 0 0) 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . x13) (x1 (λ x11 x12 . λ x13 : ι → ι → ι . setsum 0 0) (x2 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . 0) 0)))) 0 (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . x6 (λ x11 : (ι → ι) → ι → ι . 0) (x6 (λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) 0) (Inj1 0) (λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0 (λ x12 . 0) 0)) (λ x11 . Inj1 (x2 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0) 0))) (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . Inj1 0) 0 (λ x12 . x9) (x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0 (λ x12 . 0) 0)) 0) (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x0 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . 0) (x11 0 0) (Inj0 0) (λ x12 : ι → ι . λ x13 . 0)) (setsum (x6 (λ x9 : (ι → ι) → ι → ι . 0) 0 (λ x9 . 0)) 0)) (λ x9 : ι → ι . λ x10 . x10)) (λ x9 : ι → ι . λ x10 . 0) = x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . x3 (λ x11 x12 x13 . Inj1 (setsum (Inj0 0) 0)) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . Inj1 (x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . x3 (λ x15 x16 x17 . 0) (λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : ι → ι → ι . 0)) (x2 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 x16 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0) x9 (λ x13 : ι → ι . λ x14 . Inj1 0)))) (setsum 0 (x6 (λ x9 : (ι → ι) → ι → ι . x2 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x2 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . λ x16 x17 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) 0) (x2 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0) 0)) (x3 (λ x9 x10 x11 . x0 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . setsum 0 0)) (λ x9 . 0))) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . 0) x5 (setsum x5 (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . 0) 0)) (λ x9 : ι → ι . λ x10 . Inj0 (setsum 0 0))) (x2 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 . x10 (x3 (λ x13 x14 x15 . 0) (λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι → ι . 0)) (λ x13 . 0) (x2 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 x16 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . setsum 0 0) 0) (λ x9 : ι → ι . λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x13 : ι → ι . λ x14 . 0)) 0) (x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) 0) (λ x11 . 0))) (λ x9 : ι → ι . λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . setsum (x1 (λ x12 x13 . λ x14 : ι → ι → ι . x13) (x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0 (λ x12 . 0) 0)) 0) (x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . setsum 0 (x1 (λ x14 x15 . λ x16 : ι → ι → ι . 0) 0)) 0 (λ x11 . x3 (λ x12 x13 x14 . 0) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . setsum 0 0)) 0) (λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . λ x17 : ι → ι → ι . setsum 0 0) 0) (x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x3 (λ x15 x16 x17 . 0) (λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : ι → ι → ι . 0)) x10 (λ x12 . Inj0 0) (x3 (λ x12 x13 x14 . 0) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . 0))) (λ x12 . x12) 0))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . Inj1 0) (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum (x3 (λ x11 x12 x13 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . 0)) 0) (λ x9 : ι → ι . x3 (λ x10 x11 x12 . x11) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . 0)) (λ x9 . x6 (λ x10 . x9) (λ x10 x11 . 0) (λ x10 . x7))) (x3 (λ x9 x10 x11 . Inj1 x10) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . 0) (Inj1 0) 0 (λ x11 : ι → ι . λ x12 . Inj1 0))) (λ x9 : ι → ι . λ x10 . x9 0)) (setsum (Inj1 (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) 0) x4 (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0) (λ x9 : ι → ι . 0) (λ x9 . 0)) (λ x9 : ι → ι . λ x10 . Inj0 0))) 0) (λ x9 : ι → ι . λ x10 . x10) = x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . Inj1 (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . x1 (λ x15 x16 . λ x17 : ι → ι → ι . 0) 0) (x10 (λ x13 : ι → ι . λ x14 . 0)) (Inj1 0) (λ x13 : ι → ι . λ x14 . Inj1 0)) (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . x10 (λ x13 : ι → ι . λ x14 . 0)) x7 (x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) 0) (λ x11 : ι → ι . λ x12 . 0)) (Inj1 (x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) 0)) (λ x11 : ι → ι . λ x12 . 0))) (x2 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 . setsum x12 (Inj0 x12)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0) x4) (Inj1 (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum (setsum 0 0) (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0))) (λ x9 : ι → ι . x9 0) (λ x9 . x1 (λ x10 x11 . λ x12 : ι → ι → ι . x9) (setsum 0 0)))) (λ x9 : ι → ι . λ x10 . x10)) ⟶ False |
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