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