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