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