| ∀ x0 : (((ι → ι → ι) → ι) → (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι) → ι → ι . ∀ x2 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → (ι → ι → ι) → ι) → ((ι → ι → ι) → ι) → (ι → ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x10 : ι → ι . x7 x6 (setsum (x10 x6) (x1 (λ x11 . x10 0) 0))) (λ x9 . λ x10 : ι → ι → ι . x0 (λ x11 : (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 : ι → ι . setsum (x12 (λ x15 : ι → ι . Inj0 0) (λ x15 . 0) (Inj0 0)) (x13 0)) (x3 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x12 : ι → ι . x11 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . setsum 0 0) (x0 (λ x13 : (ι → ι → ι) → ι . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 x16 : ι → ι . 0) 0) (λ x13 . x2 (λ x14 : (ι → ι) → ι . 0) 0) (x1 (λ x13 . 0) 0)) (λ x11 . λ x12 : ι → ι → ι . x12 (x10 0 0) 0) (λ x11 : ι → ι → ι . x7 (setsum 0 0) (x10 0 0)) (λ x11 x12 . 0))) (λ x9 : ι → ι → ι . x1 (λ x10 . 0) 0) (λ x9 x10 . setsum x10 x10) = x1 (λ x9 . setsum (x3 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x11 : ι → ι . x0 (λ x12 : (ι → ι → ι) → ι . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 x15 : ι → ι . 0) (Inj1 0)) (λ x10 . λ x11 : ι → ι → ι . x7 0 (Inj1 0)) (λ x10 : ι → ι → ι . setsum (setsum 0 0) (Inj1 0)) (λ x10 x11 . x10)) (setsum (x0 (λ x10 : (ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 : ι → ι . setsum 0 0) 0) (Inj0 (x1 (λ x10 . 0) 0)))) x6) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x10 : ι → ι . Inj1 0) (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 : ι → ι → ι . x6 (λ x10 : (ι → ι) → ι . 0) (λ x10 . x2 (λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 . 0) 0) 0)) (λ x10 . x10) 0) (λ x9 x10 . 0) = Inj0 (x1 (λ x9 . 0) (x3 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x10 : ι → ι . x1 (λ x11 . 0) (x2 (λ x11 : (ι → ι) → ι . 0) 0)) (λ x9 . λ x10 : ι → ι → ι . x9) (λ x9 : ι → ι → ι . setsum (Inj1 0) (x6 (λ x10 : (ι → ι) → ι . 0) (λ x10 x11 . 0) (λ x10 . 0) 0)) (λ x9 x10 . x7)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ι . x2 (λ x9 : (ι → ι) → ι . x3 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x11 : ι → ι . x9 (λ x12 . setsum 0 (Inj1 0))) (λ x10 . λ x11 : ι → ι → ι . x9 (λ x12 . x0 (λ x13 : (ι → ι → ι) → ι . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 x16 : ι → ι . Inj0 0) (x3 (λ x13 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 . λ x14 : ι → ι → ι . 0) (λ x13 : ι → ι → ι . 0) (λ x13 x14 . 0)))) (λ x10 : ι → ι → ι . x0 (λ x11 : (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 : ι → ι . x2 (λ x15 : (ι → ι) → ι . setsum 0 0) (setsum 0 0)) 0) (λ x10 x11 . x7 (λ x12 . Inj0 0))) 0 = setsum 0 (x1 (λ x9 . 0) (Inj0 (setsum (Inj0 0) (x0 (λ x9 : (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι) → ι . x1 (λ x10 . setsum 0 (x0 (λ x11 : (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 : ι → ι . 0) 0)) 0) x5 = Inj1 (x6 x7)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x1 (λ x9 . x6 (x3 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 : ι → ι → ι . x3 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x12 : ι → ι . setsum 0 0) (λ x11 . λ x12 : ι → ι → ι . x11) (λ x11 : ι → ι → ι . x10 0 0) (λ x11 x12 . x3 (λ x13 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 . λ x14 : ι → ι → ι . 0) (λ x13 : ι → ι → ι . 0) (λ x13 x14 . 0))) (λ x10 x11 . x9))) (Inj0 x5) = x6 (x1 (λ x9 . x5) (Inj0 x5))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x1 (λ x9 . x9) (x4 x7) = setsum (Inj0 (x1 (λ x9 . setsum (x1 (λ x10 . 0) 0) (x1 (λ x10 . 0) 0)) 0)) 0) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 : ι → ι . Inj0 (x9 (λ x13 x14 . 0))) 0 = x4) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 : (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 : ι → ι . x10 (λ x13 : ι → ι . x0 (λ x14 : (ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 : ι → ι . x3 (λ x18 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x19 : ι → ι . 0) (λ x18 . λ x19 : ι → ι → ι . 0) (λ x18 : ι → ι → ι . x0 (λ x19 : (ι → ι → ι) → ι . λ x20 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x21 x22 : ι → ι . 0) 0) (λ x18 x19 . 0)) (x11 (x0 (λ x14 : (ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 : ι → ι . 0) 0))) (λ x13 . setsum (x0 (λ x14 : (ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 : ι → ι . x16 0) x13) 0) (Inj1 (x11 0))) (setsum 0 0) = Inj0 (x3 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x10 : ι → ι . Inj1 (x1 (λ x11 . x7 0) (x1 (λ x11 . 0) 0))) (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 : ι → ι → ι . x6) (λ x9 x10 . 0))) ⟶ False |
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