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