Let x0 of type (CT2 ι) → ι → CT2 ι be given.
Let x1 of type (CT2 ι) → (ι → ι → (ι → ι) → ι) → ι be given.
Let x2 of type (((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → CT3 ι) → CT2 ι be given.
Let x3 of type ((ι → CT2 ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x3 (λ x8 : ι → (ι → ι → ι) → ι . setsum x5 0) 0 = setsum x7 (Inj0 x7).
Assume H1:
∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι . x3 (λ x8 : ι → (ι → ι → ι) → ι . 0) (Inj0 0) = x5.
Apply FalseE with
... ⟶ ... ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x8 : ι → ι → ι . x1 (λ x9 : ι → ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 . x1 (λ x12 : ι → ι → ι . x11) (λ x12 x13 . λ x14 : ι → ι . setsum 0 0))) (λ x9 x10 . λ x11 : ι → ι . setsum (x0 (λ x12 : ι → ι → ι . 0) (setsum 0 0) (λ x12 x13 . 0)) 0)) (λ x8 x9 . λ x10 : ι → ι . x0 (λ x11 : ι → ι → ι . 0) 0 (λ x11 x12 . x12)) = x1 (λ x8 : ι → ι → ι . setsum (x3 (λ x9 : ι → (ι → ι → ι) → ι . x1 (λ x10 : ι → ι → ι . x8 0 0) (λ x10 x11 . λ x12 : ι → ι . 0)) x6) (setsum 0 0)) (λ x8 x9 . ...)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι . x1 (λ x8 : ι → ι → ι . 0) (λ x8 x9 . λ x10 : ι → ι . setsum (x7 (λ x11 : (ι → ι) → ι → ι . x0 (λ x12 : ι → ι → ι . x9) 0 (λ x12 x13 . setsum 0 0)) 0 (λ x11 . setsum (Inj1 0) x8) (x2 (λ x11 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 . x2 (λ x13 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x14 : ι → ι → ι → ι . 0) (λ x13 x14 . 0)))) x8) = x5 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . x0 (λ x8 : ι → ι → ι . x7 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι → ι . setsum 0 0) (λ x12 x13 . Inj0 (x2 (λ x14 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x15 : ι → ι → ι → ι . 0) (λ x14 x15 . 0)))) (λ x9 x10 . x7 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : ι → ι → ι . x3 (λ x15 : ι → (ι → ι → ι) → ι . 0) 0) (λ x14 x15 . λ x16 : ι → ι . Inj0 0)) (λ x11 x12 . x0 (λ x13 : ι → ι → ι . 0) (Inj0 0) (λ x13 x14 . setsum 0 0)))) x5 (λ x8 x9 . x0 (λ x10 : ι → ι → ι . Inj1 x8) x6 (λ x10 x11 . 0)) = Inj1 (x1 (λ x8 : ι → ι → ι . x8 (x0 (λ x9 : ι → ι → ι . x0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 x11 . 0)) (setsum 0 0) (λ x9 x10 . x2 (λ x11 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 . 0))) (x1 (λ x9 : ι → ι → ι . x6) (λ x9 x10 . λ x11 : ι → ι . x10))) (λ x8 x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι → ι . x0 (λ x8 : ι → ι → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι . x6 (λ x10 . x9 (x2 (λ x11 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 . 0)) (λ x11 x12 . 0))) (x6 (λ x9 . Inj1 (x1 (λ x10 : ι → ι → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0))))) (x6 (λ x8 . 0)) (λ x8 x9 . x8) = x6 (λ x8 . x8)) ⟶ False.