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