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