Let x0 of type (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 be given.
Let x2 of type ((ι → ι) → ι → ι) → (ι → CT2 ι) → ι be given.
Let x3 of type ((ι → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 x5 x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x3 (λ x8 : ι → ((ι → ι) → ι → ι) → ι . setsum (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . setsum x11 (setsum 0 0)) (λ x9 . x6)) (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum (x10 0) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) x4 = setsum (Inj0 0) (setsum (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . x7 (λ x10 : ι → ι → ι . λ x11 : ι → ι . Inj0 0))) 0).
Assume H1:
∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x8 : ι → ((ι → ι) → ι → ι) → ι . x8 (x7 (λ x9 x10 . setsum 0 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . x10))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x11 (Inj0 0) (λ x12 : ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0))) x10)) (setsum (x0 (λ x8 x9 . x7 (λ x10 x11 . 0) (λ x10 : ι → ι . λ x11 . setsum 0 0)) (setsum (setsum 0 0) 0) 0 (λ x8 . setsum 0 0)) (x3 (λ x8 : ι → ((ι → ι) → ι → ι) → ι . x6 (λ x9 . 0)) (x7 (λ x8 x9 . setsum 0 0) (λ x8 : ι → ι . λ x9 . x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0))))) = setsum (x0 (λ x8 x9 . Inj0 (setsum x9 0)) (x3 (λ x8 : ι → ((ι → ι) → ι → ι) → ι . x8 0 (λ x9 : ι → ι . λ x10 . 0)) 0) (Inj1 (x2 (λ x8 : ι → ι . λ x9 . x6 (λ x10 . 0)) (λ x8 . λ x9 : ι → ι → ι . x9 0 0))) (λ x8 . x7 (λ x9 x10 . x9) (λ x9 : ι → ι . λ x10 . setsum (Inj1 0) x10))) 0.
Assume H2: ∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 : ι → ι . λ x9 . x8 0) (λ x8 . λ x9 : ι → ι → ι . x8) = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x0 (λ x8 x9 . x9) (Inj1 (x2 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . λ x9 : ι → ι → ι . Inj1 (x2 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . λ x11 : ι → ι → ι . 0))))) (x0 (λ x8 x9 . 0) (Inj1 (setsum 0 (x0 (λ x8 x9 . 0) 0 0 (λ x8 . 0)))) x4 (λ x8 . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 x10 . 0) (x0 (λ x9 x10 . 0) 0 0 (λ x9 . 0)) (setsum 0 0) ...))) ... = ...) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 x9 . x9) 0 (x0 (λ x8 x9 . x8) x5 (Inj0 x7) (λ x8 . x7)) (λ x8 . x7) = Inj0 (x2 (λ x8 : ι → ι . λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . x9) x7) (λ x8 . λ x9 : ι → ι → ι . 0))) ⟶ False.