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