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