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