Let x0 of type (ι → ι) → ι → ι be given.
Let x1 of type (ι → ι → (ι → ι) → ι) → ι → ι be given.
Let x2 of type (ι → ι → ((ι → ι) → ι) → (ι → ι) → ι) → CT4 ι be given.
Let x3 of type ((CT2 ι) → ι) → (ι → (ι → ι) → ι) → ι be given.
Assume H0:
∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x3 (λ x8 : (ι → ι → ι) → ι . setsum (x1 (λ x9 x10 . λ x11 : ι → ι . Inj0 x9) (x3 (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 . 0) 0) (λ x9 . λ x10 : ι → ι . x8 (λ x11 x12 . 0)))) (Inj0 (x0 (λ x9 . 0) 0))) (λ x8 . λ x9 : ι → ι . 0) = setsum (Inj0 (Inj0 (setsum x6 (setsum 0 0)))) x6.
Assume H1:
∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 : (ι → ι → ι) → ι . x6 (x2 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum (setsum 0 0) (setsum 0 0)) (λ x9 x10 x11 x12 . 0))) (λ x8 . λ x9 : ι → ι . Inj0 0) = x6 (x3 (λ x8 : (ι → ι → ι) → ι . Inj0 0) (λ x8 . λ x9 : ι → ι . 0)).
Assume H2:
∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x7 . x2 (λ x8 x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x8) (λ x8 x9 x10 x11 . x3 (λ x12 : (ι → ι → ι) → ι . x2 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0) (λ x13 x14 x15 x16 . x0 (λ x17 . Inj0 0) (Inj1 0))) (λ x12 . λ x13 : ι → ι . x2 (λ x14 x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . Inj0 (Inj0 0)) (λ x14 x15 x16 x17 . x16))) = Inj1 (x3 (λ x8 : (ι → ι → ι) → ι . x3 (λ x9 : (ι → ι → ι) → ι . setsum (x1 (λ x10 x11 . λ x12 : ι → ι . 0) 0) (x0 (λ x10 . 0) 0)) (λ x9 . λ x10 : ι → ι . x10 (x0 (λ x11 . 0) 0))) (λ x8 . λ x9 : ι → ι . x0 (λ x10 . 0) (setsum (x6 (λ x10 x11 : ι → ι . λ x12 . 0) 0) 0))).
Assume H3:
∀ x4 x5 x6 x7 . x2 (λ x8 x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x0 (λ x12 . x3 (λ x13 : (ι → ι → ι) → ι . x1 (λ x14 x15 . λ x16 : ι → ι . 0) 0) (λ x13 . λ x14 : ι → ι . x12)) (setsum 0 (setsum 0 0))) (x11 (setsum 0 0))) (λ x8 x9 x10 x11 . Inj0 (setsum (setsum (Inj1 0) x8) 0)) = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x8 . x3 (λ x9 : (ι → ι → ι) → ι . setsum 0 0) (λ x9 . λ x10 : ι → ι . setsum x8 0)) (x3 (λ x8 : (ι → ι → ι) → ι . setsum 0 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . 0))) (λ x8 . λ x9 : ι → ι . x3 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . x1 (λ x12 x13 . λ x14 : ι → ι . x3 (λ x15 : (ι → ι → ι) → ι . 0) (λ x15 . λ x16 : ι → ι . 0)) (setsum 0 0)))) = setsum (Inj1 (x2 (λ x8 x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) (λ x8 x9 x10 x11 . x3 (λ x12 : (ι → ι → ι) → ι . x9) (λ x12 . λ x13 : ι → ι . x2 (λ x14 x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) (λ x14 x15 x16 x17 . 0))))) (x5 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (x3 ... ...)))) ⟶ False.