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