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