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