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