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