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