Let x0 of type (ι → (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι) → ι → ι be given.
Let x1 of type (CT2 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 → (ι → ι) → ι → ι) → ι) → ι be given.
Assume H0:
∀ x4 : (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 x9 x10 . x10) (λ x8 : ι → (ι → ι) → ι → ι . x2 (λ x9 . x9) x7) = Inj0 0.
Assume H1:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x3 (λ x8 x9 x10 . 0) (λ x8 : ι → (ι → ι) → ι → ι . setsum (Inj0 (setsum 0 (x1 (λ x9 : ι → ι → ι . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . 0)))) (setsum 0 (x3 (λ x9 x10 x11 . 0) (λ x9 : ι → (ι → ι) → ι → ι . x3 (λ x10 x11 x12 . 0) (λ x10 : ι → (ι → ι) → ι → ι . 0))))) = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 : ι → ι → ι . x7) (λ x8 . x5 (x1 (λ x9 : ι → ι → ι . Inj1 (x1 (λ x10 : ι → ι → ι . 0) (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . 0))) (λ x9 . x2 (λ x10 . setsum 0 0) (setsum 0 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) 0) 0)) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum (setsum 0 0) (x2 (λ x13 . 0) 0)) (x2 (λ x9 . x8) x7)) (λ x9 . 0) (x1 (λ x9 : ι → ι → ι . x8) (λ x9 . x3 (λ x10 x11 x12 . x9) (λ x10 : ι → (ι → ι) → ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . x10))) (λ x8 : (ι → ι) → ι → ι . λ x9 . setsum (Inj1 (x0 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x3 (λ x14 x15 x16 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0)) (x2 (λ x10 . 0) 0))) (x3 (λ x10 x11 x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0) x9) (λ x10 : ι → (ι → ι) → ι → ι . setsum 0 0))) = x5 (Inj0 (Inj1 (x3 (λ x8 x9 x10 . setsum 0 0) (λ x8 : ι → (ι → ι) → ι → ι . Inj0 0)))) (x1 (λ x8 : ι → ι → ι . x1 (λ x9 : ι → ι → ι . x1 (λ x10 : ι → ι → ι . x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) 0) (λ x10 . x2 (λ x11 . 0) 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . x10 (λ x12 . 0) 0)) (λ x9 . x8 (setsum 0 0) x9) (λ x9 : (ι → ι) → ι → ι . λ x10 . ...)) ... ...) ... ...) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x0 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . Inj1 (x1 (λ x12 : ι → ι → ι . x9 (λ x13 : ι → ι . λ x14 . Inj0 0)) (λ x12 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 . x13))) 0 = Inj0 x4) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 : ι → ι . x0 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) (setsum (x4 (x1 (λ x8 : ι → ι → ι . x2 (λ x9 . 0) 0) (λ x8 . x1 (λ x9 : ι → ι → ι . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . 0)) (λ x8 : (ι → ι) → ι → ι . λ x9 . 0))) 0) = x5) ⟶ False.