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