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