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