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