Let x0 of type (ι → ((ι → ι) → ι → ι) → ι) → ((CT2 ι) → ι) → (((ι → ι) → ι) → ι) → ι → ι be given.
Let x1 of type (ι → (ι → ι) → ι) → ι → ι → ι be given.
Let x2 of type (ι → (((ι → ι) → ι → ι) → ι → ι → ι) → ι) → (ι → ι) → ι be given.
Let x3 of type ((ι → ι) → (((ι → ι) → ι) → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . x8 (x0 (λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι) → ι . 0) 0) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . 0))) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . 0) (setsum 0 0))) (setsum (x5 (λ x8 . Inj1 (setsum 0 0)) (λ x8 : ι → ι . 0)) x7) = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 x6 x7 . x0 (λ x8 . λ x9 : (ι → ι) → ι → ι . x0 (λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x13 . 0)) (λ x11 . x1 (λ x12 . λ x13 : ι → ι . 0) (x10 (λ x12 x13 . 0)) 0)) (λ x10 : (ι → ι) → ι . x1 (λ x11 . λ x12 : ι → ι . x10 (λ x13 . Inj1 0)) (setsum (setsum 0 0) (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x11 . 0))) (Inj0 (x9 (λ x11 . 0) 0))) (setsum (setsum x8 0) 0)) (λ x8 : (ι → ι → ι) → ι . Inj1 0) (λ x8 : (ι → ι) → ι . 0) 0 = x0 (λ x8 . λ x9 : (ι → ι) → ι → ι . setsum (x0 (λ x10 . λ x11 : (ι → ι) → ι → ι . Inj0 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . x10 (λ x11 . x1 (λ x12 . λ x13 : ι → ι . 0) 0 0)) (Inj1 x6)) (x0 (λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) (Inj1 0)) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . Inj0 0)) (λ x10 : (ι → ι) → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x13 . λ x14 : ι → ι . 0) 0 0) (λ x11 . setsum 0 0)) (Inj1 ...))) ... ... ...) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 . λ x9 : (ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . 0) 0 (x0 (λ x10 . λ x11 : (ι → ι) → ι → ι . setsum (x0 (λ x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0) 0) (x1 (λ x12 . λ x13 : ι → ι . 0) 0 0)) (λ x10 : (ι → ι → ι) → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . x9 (λ x13 . 0) 0) (λ x11 . setsum 0 0)) (λ x10 : (ι → ι) → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . x10 (λ x13 . 0)) (λ x11 . setsum 0 0)) x7)) (λ x8 : (ι → ι → ι) → ι . x6) (λ x8 : (ι → ι) → ι . x6) 0 = Inj1 (x0 (λ x8 . λ x9 : (ι → ι) → ι → ι . setsum 0 (x0 (λ x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι) → ι . 0) 0) (λ x10 : (ι → ι → ι) → ι . x9 (λ x11 . 0) 0) (λ x10 : (ι → ι) → ι . setsum 0 0) x6)) (λ x8 : (ι → ι → ι) → ι . x8 (λ x9 x10 . x8 (λ x11 x12 . x9))) (λ x8 : (ι → ι) → ι . Inj0 (Inj1 (setsum 0 0))) 0)) ⟶ False.