| ∀ x0 : ((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) → 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 . ∀ x3 : (ι → ι → ι) → (ι → ι) → ι . (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 x10 . 0) (λ x9 . 0) = Inj1 (setsum (x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . x13) (Inj0 0)) x5)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 : ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x9 x10 . x7 (λ x11 . setsum (x7 (λ x12 . x3 (λ x13 x14 . 0) (λ x13 . 0)) (λ x12 x13 . 0) (Inj0 0)) x10) (λ x11 x12 . Inj1 (x1 (λ x13 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x14 x15 x16 x17 . x16) (x1 (λ x13 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x14 x15 x16 x17 . 0) 0))) (x6 (Inj0 0))) (λ x9 . 0) = x7 (λ x9 . setsum 0 (x0 (λ x10 : ι → ((ι → ι) → ι) → ι . x1 (λ x11 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x12 x13 x14 x15 . x2 (λ x16 . λ x17 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x16 : ((ι → ι) → ι → ι) → ι → ι . λ x17 x18 . 0)) 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj1 (x2 (λ x14 . λ x15 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . 0))) 0 (x6 0) (λ x10 . Inj0 (setsum 0 0)) (x0 (λ x10 : ι → ((ι → ι) → ι) → ι . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (setsum 0 0) (x7 (λ x10 . 0) (λ x10 x11 . 0) 0) (λ x10 . x7 (λ x11 . 0) (λ x11 x12 . 0) 0) 0))) (λ x9 x10 . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι) → ι → ι → ι . x0 (λ x13 : ι → ((ι → ι) → ι) → ι . x11) (λ x13 x14 . λ x15 : ι → ι . λ x16 . x14) (x2 (λ x13 . λ x14 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . 0)) (x12 (λ x13 : ι → ι . 0) 0 0) (λ x13 . x0 (λ x14 : ι → ((ι → ι) → ι) → ι . 0) (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) 0 0 (λ x14 . 0) 0) 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι . λ x12 x13 . 0)) (x3 (λ x11 x12 . 0) (λ x11 . x10))) (x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . Inj1 (x3 (λ x14 x15 . Inj0 0) (λ x14 . setsum 0 0))) (setsum (x3 (λ x9 x10 . x10) (λ x9 . Inj0 0)) (setsum (setsum 0 0) (x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 . λ x10 : ((ι → ι) → ι) → ι → ι → ι . x10 (λ x11 : ι → ι . x3 (λ x12 x13 . Inj0 (x11 0)) (λ x12 . x1 (λ x13 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x14 x15 x16 x17 . x1 (λ x18 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x19 x20 x21 x22 . 0) 0) (setsum 0 0))) (Inj0 x9) 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . 0) = x6 (λ x9 : ι → ι . 0) 0 (λ x9 . x6 (λ x10 : ι → ι . x7) (x2 (λ x10 . λ x11 : ((ι → ι) → ι) → ι → ι → ι . Inj1 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . 0)) (λ x10 . 0))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . x11) = x7 (λ x9 . x2 (λ x10 . λ x11 : ((ι → ι) → ι) → ι → ι → ι . setsum (x0 (λ x12 : ι → ((ι → ι) → ι) → ι . x2 (λ x13 . λ x14 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . 0)) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 x17 . 0) (λ x16 . 0)) 0 (x3 (λ x12 x13 . 0) (λ x12 . 0)) (λ x12 . 0) x9) (x11 (λ x12 : ι → ι . x3 (λ x13 x14 . 0) (λ x13 . 0)) (x7 (λ x12 . 0)) x9)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι) → ι → ι → ι . x13) (λ x13 : ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . setsum (x2 (λ x16 . λ x17 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x16 : ((ι → ι) → ι → ι) → ι → ι . λ x17 x18 . 0)) (setsum 0 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . 0) 0 = x4 (λ x9 . λ x10 : ι → ι . 0) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . Inj0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . setsum x10 (Inj0 (x11 0))) x6 (setsum x6 (x7 (λ x9 . x7 (λ x10 . 0)))) (λ x9 . 0))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι . x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . x1 (λ x14 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x15 x16 x17 x18 . x1 (λ x19 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x20 x21 x22 x23 . Inj1 0) (Inj1 (x1 (λ x19 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x20 x21 x22 x23 . 0) 0))) x11) (x2 (λ x9 . λ x10 : ((ι → ι) → ι) → ι → ι → ι . x3 (λ x11 x12 . Inj0 (x0 (λ x13 : ι → ((ι → ι) → ι) → ι . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) 0 0 (λ x13 . 0) 0)) (λ x11 . 0)) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . Inj1 0)) = setsum x5 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x9 : ι → ((ι → ι) → ι) → ι . Inj0 (x2 (λ x10 . λ x11 : ((ι → ι) → ι) → ι → ι → ι . Inj1 (setsum 0 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . Inj0 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x12) 0 0 (λ x9 . 0) (x3 (λ x9 x10 . x3 (λ x11 x12 . x3 (λ x13 x14 . x12) (λ x13 . 0)) (λ x11 . x7 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → ι . x9) (λ x12 . x1 (λ x13 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x14 x15 x16 x17 . 0) 0) 0)) (λ x9 . 0)) = Inj1 (Inj0 (setsum (setsum (x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . 0) 0) (x2 (λ x9 . λ x10 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . 0))) (x6 (λ x9 . x0 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) 0 0 (λ x10 . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → ((ι → ι) → ι) → ι . setsum (setsum (setsum (x1 (λ x10 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x11 x12 x13 x14 . 0) 0) (x2 (λ x10 . λ x11 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . 0))) (Inj0 (setsum 0 0))) (Inj1 (Inj0 (x0 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) 0 0 (λ x10 . 0) 0)))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . setsum 0 (x2 (λ x13 . λ x14 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . x2 (λ x16 . λ x17 : ((ι → ι) → ι) → ι → ι → ι . x15) (λ x16 : ((ι → ι) → ι → ι) → ι → ι . λ x17 x18 . x17)))) (Inj0 0) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . Inj0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . setsum x12 (x1 (λ x13 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x14 x15 x16 x17 . x14) (x1 (λ x13 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x14 x15 x16 x17 . 0) 0))) (Inj0 x7) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . setsum (x0 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) 0 0 (λ x10 . 0) 0) 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 (Inj0 0)) (x4 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . Inj0 0) x6) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x12) 0 (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) 0 0 (λ x9 . 0) 0) (λ x9 . Inj1 0) 0) (λ x9 . x3 (λ x10 x11 . 0) (λ x10 . setsum 0 0)) 0) (λ x9 . 0) (x1 (λ x9 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x10 x11 x12 x13 . x3 (λ x14 x15 . setsum 0 0) (λ x14 . x0 (λ x15 : ι → ((ι → ι) → ι) → ι . 0) (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) 0 0 (λ x15 . 0) 0)) 0)) (λ x9 . 0) (x2 (λ x9 . λ x10 : ((ι → ι) → ι) → ι → ι → ι . setsum (x3 (λ x11 x12 . 0) (λ x11 . setsum 0 0)) 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 : ι → ι . λ x13 . Inj1 (setsum 0 0)) x7)) = Inj1 (setsum x7 (Inj0 x7))) ⟶ False |
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