Let x0 of type (CT2 ι) → ι → (ι → ι) → ι be given.
Let x1 of type (ι → ((ι → ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ι) → (((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 be given.
Assume H0:
∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι → ι . x3 (λ x8 . x7 (λ x9 : ι → ι → ι . λ x10 . 0) (x3 (λ x9 . x6) x8 (Inj1 0))) (x2 (λ x8 . x3 (λ x9 . 0) (setsum (x3 (λ x9 . 0) 0 0) 0) (x3 (λ x9 . x2 (λ x10 . 0) 0) x5 (x2 (λ x9 . 0) 0))) (x4 (λ x8 : (ι → ι) → ι . x8 (λ x9 . x0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 . 0))))) x6 = setsum 0 (x4 (λ x8 : (ι → ι) → ι . Inj1 x6)).
Assume H1:
∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x8 . setsum x8 x8) (x4 (x5 (λ x8 : (ι → ι) → ι . 0))) (Inj0 (x2 (λ x8 . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x9 : ι → ι . x8) (λ x9 : (ι → ι) → ι . x6) (setsum 0 0)) (x1 (λ x8 . λ x9 : (ι → ι → ι) → ι → ι . λ x10 . setsum 0 0) (λ x8 : ι → ι . x3 (λ x9 . 0) 0 0) (λ x8 : (ι → ι) → ι . x2 (λ x9 . 0) 0) 0))) = x4 (x7 0).
Assume H2:
∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 x7 : ι → ι . x2 (λ x8 . x2 (λ x9 . x8) 0) (x2 (λ x8 . 0) (x5 (Inj0 (x2 (λ x8 . 0) 0)) (λ x8 : ι → ι . x7 (x3 (λ x9 . 0) 0 0)) (λ x8 . x3 (λ x9 . 0) (x6 0) 0))) = x2 (λ x8 . Inj0 (setsum x8 (setsum x8 0))) (setsum 0 (x4 (λ x8 . x3 (λ x9 . Inj0 0) (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (x7 0)) (λ x8 . x3 (λ x9 . 0) (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (x0 (λ x9 : ι → ι → ι . 0) 0 (λ x9 . 0))))).
Assume H3: ∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι → ι → ι . x2 (λ x8 . 0) 0 = x5.
Apply FalseE with
... ⟶ ... ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι → ι . x0 (λ x8 : ι → ι → ι . x5) (x1 (λ x8 . λ x9 : (ι → ι → ι) → ι → ι . λ x10 . Inj1 (x3 (λ x11 . 0) 0 (x1 (λ x11 . λ x12 : (ι → ι → ι) → ι → ι . λ x13 . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0) 0))) (λ x8 : ι → ι . Inj0 (x2 (λ x9 . x9) ...)) ... ...) ... = ...) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x8 : ι → ι → ι . 0) (x7 (x3 (λ x8 . x2 (λ x9 . x3 (λ x10 . 0) 0 0) (Inj0 0)) (setsum 0 x5) 0)) (λ x8 . x8) = x7 (setsum 0 0)) ⟶ False.