Let x0 of type ((ι → 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) → (CT3 ι) → ι → ι be given.
Let x3 of type (ι → ι → ι → ι) → ι → ι be given.
Assume H0:
∀ x4 x5 x6 x7 . x3 (λ x8 x9 x10 . x1 (λ x11 : ((ι → ι) → ι) → ι . x2 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . setsum x10 (Inj0 0)) 0) (x1 (λ x11 : ((ι → ι) → ι) → ι . x3 (λ x12 x13 x14 . 0) 0) 0)) 0 = setsum x4 x6.
Assume H1:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 x9 x10 . 0) x6 = Inj1 (Inj0 (x1 (λ x8 : ((ι → ι) → ι) → ι . Inj1 0) (setsum 0 0))).
Assume H2: ∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 . 0) (λ x8 : ι → ι → ι → ι . x8 0 (x1 (λ x9 : ((ι → ι) → ι) → ι . 0) 0) (x3 (λ x9 x10 x11 . x0 (λ x12 : ι → ι . x0 (λ x13 : ι → ι . 0) 0) 0) x5)) 0 = x7.
Apply FalseE with
(∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι . x2 (λ x8 . 0) (λ x8 : ι → ι → ι → ι . 0) (x7 (λ x8 : (ι → ι) → ι . x2 (λ x9 . setsum (x8 (λ x10 . 0)) x9) (λ x9 : ι → ι → ι → ι . 0) (x0 (λ x9 : ι → ι . x0 (λ x10 : ι → ι . 0) 0) 0)) ... 0) = ...) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 x7 . x1 (λ x8 : ((ι → ι) → ι) → ι . x6) 0 = x6) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x8 : ((ι → ι) → ι) → ι . x0 (λ x9 : ι → ι . x2 (λ x10 . x3 (λ x11 x12 x13 . 0) (Inj0 0)) (λ x10 : ι → ι → ι → ι . x0 (λ x11 : ι → ι . Inj1 0) (Inj1 0)) (setsum (Inj0 0) (x2 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0))) (x8 (λ x9 : ι → ι . Inj0 0))) (x1 (λ x8 : ((ι → ι) → ι) → ι . x0 (λ x9 : ι → ι . x8 (λ x10 : ι → ι . x10 0)) (x8 (λ x9 : ι → ι . x1 (λ x10 : ((ι → ι) → ι) → ι . 0) 0))) x6) = setsum x7 (Inj0 x6)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x8 : ι → ι . setsum (setsum 0 0) (x0 (λ x9 : ι → ι . x3 (λ x10 x11 x12 . x10) 0) (x5 x7 0))) (x2 (λ x8 . Inj0 x8) (λ x8 : ι → ι → ι → ι . x3 (λ x9 x10 x11 . x3 (λ x12 x13 x14 . x0 (λ x15 : ι → ι . 0) 0) (Inj1 0)) (x5 0 (setsum 0 0))) 0) = x2 (λ x8 . setsum (x0 (λ x9 : ι → ι . x8) (x3 (λ x9 x10 x11 . 0) (setsum 0 0))) (x1 (λ x9 : ((ι → ι) → ι) → ι . setsum (x3 (λ x10 x11 x12 . 0) 0) 0) 0)) (λ x8 : ι → ι → ι → ι . setsum (x0 (λ x9 : ι → ι . setsum x7 (setsum 0 0)) (x5 x7 (x5 0 0))) x7) (x0 (λ x8 : ι → ι . 0) x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x8 : ι → ι . 0) x5 = setsum 0 (x4 0)) ⟶ False.