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