Let x0 of type (ι → ι) → CT2 ι be given.
Let x1 of type (((CN (ι → ι)) → ι) → ((ι → ι) → (ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι be given.
Let x2 of type ((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) → ι → ι) → ι → (ι → ι) → ι → ι → ι) → ι → ι be given.
Assume H0:
∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x3 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . λ x11 x12 . 0) (Inj1 (x1 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι → ι . x3 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 x14 . 0) (x9 (λ x10 . 0) (λ x10 . 0) 0)) (λ x8 : ι → ι . λ x9 . Inj1 (x2 (λ x10 : ι → ι . λ x11 . 0) 0 (λ x10 : ι → ι . λ x11 . 0))))) = setsum (Inj0 (Inj0 (x3 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . λ x11 x12 . setsum 0 0) (x1 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι → ι . 0) (λ x8 : ι → ι . λ x9 . 0))))) (Inj1 (x7 (x7 (Inj0 0) 0 (λ x8 . x6 (λ x9 : (ι → ι) → ι . 0) (λ x9 . 0) 0)) 0 (λ x8 . setsum (Inj0 0) (setsum 0 0)))).
Assume H1:
∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . λ x11 x12 . x12) (setsum (x0 (λ x8 . x2 (λ x9 : ι → ι . λ x10 . 0) (Inj1 0) (λ x9 : ι → ι . λ x10 . setsum 0 0)) (λ x8 x9 . x8)) (x2 (λ x8 : ι → ι . λ x9 . Inj1 (x0 (λ x10 . 0) (λ x10 x11 . 0))) (setsum (x6 0) (x0 (λ x8 . 0) (λ x8 x9 . 0))) (λ x8 : ι → ι . λ x9 . setsum (Inj0 0) 0))) = x7.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι → ι . 0) (λ x8 : ι → ι . λ x9 . 0) = setsum 0 (setsum (x6 (λ x8 x9 x10 . x10) (x1 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι → ι . x7 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0) (λ x10 : ι → ι . λ x11 . 0)) (λ x8 : ι → ι . λ x9 . 0))) (x0 (λ x8 . x8) (λ x8 x9 . setsum (x2 (λ x10 : ι → ι . λ x11 . 0) 0 (λ x10 : ι → ι . λ x11 . 0)) (x7 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0) (λ x10 : ι → ι . λ x11 . 0)))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x7 . x0 (λ x8 . x5 0) (λ x8 x9 . 0) = setsum 0 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x0 (λ x8 . x2 (λ x9 : ι → ι . λ x10 . setsum 0 x8) (x0 (λ x9 . setsum (x7 (λ x10 x11 x12 . 0)) (setsum 0 0)) (λ x9 x10 . x9)) (λ x9 : ι → ι . λ x10 . x7 (λ x11 x12 x13 . x2 (λ x14 : ι → ι . λ x15 . x13) (Inj1 0) (λ x14 : ι → ι . λ x15 . x15)))) (λ x8 x9 . x7 (λ x10 x11 x12 . x0 (λ x13 . 0) (λ x13 x14 . Inj0 (x0 (λ x15 . 0) (λ x15 x16 . 0))))) = Inj1 (x0 (λ x8 . 0) (λ x8 x9 . 0))) ⟶ False.