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