Let x0 of type (ι → ι) → ι → ι → ι → ι be given.
Let x1 of type (ι → ι) → ι → ι be given.
Let x2 of type ((CT2 ι) → ι) → (((ι → ι) → ι) → ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι be given.
Let x3 of type (ι → ι → ι) → ι → ι be given.
Assume H0:
∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 x9 . setsum (setsum 0 0) (x0 (λ x10 . x7) (Inj1 (Inj1 0)) x7 x9)) 0 = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x8 . setsum x8 (Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . x7 (λ x10 : (ι → ι) → ι → ι . 0))))) (x1 (λ x8 . x6) (setsum 0 (x7 (λ x8 : (ι → ι) → ι → ι . 0)))) = Inj1 (x1 (λ x8 . x0 (λ x9 . x9) x5 (x2 (λ x9 : (ι → ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . λ x10 . x7 (λ x11 : (ι → ι) → ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum 0 0)) (setsum 0 0)) (x2 (λ x8 : (ι → ι → ι) → ι . x5) (λ x8 : (ι → ι) → ι . λ x9 . x1 ... ...) ...))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . x0 (λ x8 . x8) (x6 x4) x4 (setsum x4 x4) = setsum (x0 (λ x8 . x5 (x2 (λ x9 : (ι → ι → ι) → ι . x8) (λ x9 : (ι → ι) → ι . λ x10 . x9 (λ x11 . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) (λ x9 : ι → ι . λ x10 . x10) 0) (setsum 0 (x6 0)) (x5 (Inj1 (Inj1 0)) (λ x8 : ι → ι . λ x9 . x1 (λ x10 . x1 (λ x11 . 0) 0) (x6 0)) x4) (x1 (λ x8 . 0) (x7 (λ x8 : ι → ι . x2 (λ x9 : (ι → ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . λ x10 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) (λ x8 x9 . x9) (λ x8 . x5 0 (λ x9 : ι → ι . λ x10 . 0) 0)))) (setsum (Inj1 (x3 (λ x8 x9 . 0) 0)) (x1 (λ x8 . setsum (x1 (λ x9 . 0) 0) 0) (x3 (λ x8 x9 . x2 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 . 0) 0 0 (x2 (λ x8 : (ι → ι → ι) → ι . x5) (λ x8 : (ι → ι) → ι . λ x9 . 0) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . x8 (λ x10 . x0 (λ x11 . setsum 0 0) (x3 (λ x11 x12 . 0) 0) (x2 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) 0) 0)) = x2 (λ x8 : (ι → ι → ι) → ι . x8 (λ x9 x10 . 0)) (λ x8 : (ι → ι) → ι . λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . setsum (x0 (λ x11 . x10 (λ x12 x13 . 0)) (Inj0 0) (x1 (λ x11 . 0) 0) 0) x9) (λ x10 : (ι → ι) → ι . λ x11 . Inj1 (x1 (λ x12 . x9) x9)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . Inj0 (x8 (λ x10 . 0) x6))) ⟶ False.