Let x0 of type ((CT3 ι) → ι) → ι → ι be given.
Let x1 of type ((ι → ι) → ι) → (((ι → ι → ι) → ι → ι) → ι) → ι be given.
Let x2 of type (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 : ι → ι . ∀ x5 x6 x7 . x3 (λ x8 . Inj1 (x1 (λ x9 : ι → ι . x8) (λ x9 : (ι → ι → ι) → ι → ι . setsum 0 (x2 (λ x10 . 0) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0))))) x7 0 = setsum (x0 (λ x8 : (ι → ι → ι → ι) → ι . x2 (λ x9 . setsum 0 x7) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x0 (λ x13 : (ι → ι → ι → ι) → ι . x3 (λ x14 . 0) 0 0) (setsum 0 0))) (setsum (Inj1 x6) x6)) 0.
Assume H1:
∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x8 . setsum x8 x8) 0 (x2 (λ x8 . x2 (λ x9 . x7 (setsum 0 0) (x3 (λ x10 . 0) 0 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0)) (λ x8 . λ x9 : ι → ι → ι . λ x10 x11 . Inj0 (setsum (Inj1 0) x8))) = x2 (λ x8 . x0 (λ x9 : (ι → ι → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι → ι) → ι . 0) 0) 0) (λ x8 . λ x9 : ι → ι → ι . λ x10 x11 . x9 (x1 (λ x12 : ι → ι . x9 0 0) (λ x12 : (ι → ι → ι) → ι → ι . 0)) 0).
Assume H2:
∀ x4 : ι → ι → ι → ι . ∀ x5 x6 x7 : ι → ι . x2 (λ x8 . 0) (λ x8 . λ x9 : ι → ι → ι . λ x10 x11 . Inj1 (setsum (setsum (setsum 0 0) 0) (x9 (x2 (λ x12 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0)) 0))) = x7 (Inj1 (x1 (λ x8 : ι → ι . 0) (λ x8 : (ι → ι → ι) → ι → ι . x1 (λ x9 : ι → ι . x7 0) (λ x9 : (ι → ι → ι) → ι → ι . x0 (λ x10 : (ι → ι → ι → ι) → ι . 0) 0)))).
Apply FalseE with
(∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x8 . 0) (λ x8 . λ x9 : ι → ι → ι . λ x10 x11 . x9 ... 0) = ...) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x8 : ι → ι . setsum (x8 (x6 (λ x9 . x0 (λ x10 : (ι → ι → ι → ι) → ι . 0) 0) (λ x9 x10 . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0) (λ x9 . 0))) (x6 (λ x9 . x8 0) (λ x9 x10 . 0) (λ x9 . x9))) (λ x8 : (ι → ι → ι) → ι → ι . x2 (λ x9 . x8 (λ x10 x11 . setsum 0 0) 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 (x0 (λ x13 : (ι → ι → ι → ι) → ι . 0) (x10 0 0)))) = x2 (λ x8 . x5) (λ x8 . λ x9 : ι → ι → ι . λ x10 x11 . x9 (x0 (λ x12 : (ι → ι → ι → ι) → ι . Inj1 (x2 (λ x13 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0))) x11) 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x8 : ι → ι . setsum 0 0) (λ x8 : (ι → ι → ι) → ι → ι . x5) = x5) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : (ι → ι → ι → ι) → ι . setsum x5 (Inj0 0)) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 : (ι → ι → ι → ι) → ι . x7) x5 = x5) ⟶ False.