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