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