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