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