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