Let x0 of type (ι → ι) → (ι → CT2 ι) → ι be given.
Let x1 of type (ι → ι) → ι → ι be given.
Let x2 of type ((ι → ι → (ι → ι) → ι) → (ι → 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 be given.
Assume H0: ∀ x4 : ι → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι . x3 (λ x8 x9 x10 . x9) (λ x8 . x8) = x6 (x4 0).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : ι → ι → ι . x1 (λ x8 . 0) (x6 0 (λ x8 x9 . x0 (λ x10 . x2 (λ x11 : ι → ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x11 x12 . x11) (setsum 0 0)) (λ x10 . λ x11 : ι → ι → ι . x3 (λ x12 x13 x14 . x12) (λ x12 . 0)))) = x6 (x3 (λ x8 x9 x10 . x7 (x7 x10 (x2 (λ x11 : ι → ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 x12 . 0) 0)) (x2 (λ x11 : ι → ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 x17 x18 . 0) (λ x16 . 0)) (λ x11 x12 . x0 (λ x13 . 0) (λ x13 . λ x14 : ι → ι → ι . 0)) (Inj0 0))) (λ x8 . x7 (setsum 0 (x7 0 0)) (x7 (x5 (λ x9 . 0)) (x3 ... ...)))) ...) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x0 (λ x8 . Inj0 (x0 (λ x9 . setsum (Inj0 0) (x6 0)) (λ x9 . λ x10 : ι → ι → ι . 0))) (λ x8 . λ x9 : ι → ι → ι . 0) = Inj1 (setsum 0 (x0 (λ x8 . 0) (λ x8 . λ x9 : ι → ι → ι . x1 (λ x10 . 0) 0)))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . x0 (λ x8 . x7 (λ x9 . setsum x8 (setsum 0 x8)) (λ x9 x10 . x3 (λ x11 x12 x13 . x13) (λ x11 . Inj1 (x0 (λ x12 . 0) (λ x12 . λ x13 : ι → ι → ι . 0))))) (λ x8 . λ x9 : ι → ι → ι . x9 (x0 (λ x10 . x9 (Inj1 0) x8) (λ x10 . λ x11 : ι → ι → ι . 0)) (x1 (λ x10 . 0) 0)) = x7 (λ x8 . setsum (Inj1 x8) (x2 (λ x9 : ι → ι → (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 (setsum 0 0)) (λ x9 x10 . x3 (λ x11 x12 x13 . 0) (λ x11 . 0)) (x0 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . x2 (λ x11 : ι → ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 x12 . 0) 0)))) (λ x8 x9 . setsum (x1 (λ x10 . x3 (λ x11 x12 x13 . Inj1 0) (λ x11 . x0 (λ x12 . 0) (λ x12 . λ x13 : ι → ι → ι . 0))) (Inj0 (x3 (λ x10 x11 x12 . 0) (λ x10 . 0)))) (x2 (λ x10 : ι → ι → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . x14) (λ x10 x11 . x0 (λ x12 . Inj0 0) (λ x12 . λ x13 : ι → ι → ι . 0)) (setsum 0 (x2 (λ x10 : ι → ι → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 x11 . 0) 0))))) ⟶ False.