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