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