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