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