Let x0 of type (ι → ι) → (CT3 ι) → ι be given.
Let x1 of type (ι → (CT2 ι) → ι → (ι → ι) → ι) → ((CT2 ι) → ι) → ι → (ι → ι) → ι be given.
Let x2 of type (ι → ι → ι) → ι → ι be given.
Let x3 of type ((ι → ι → (ι → ι) → ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι) → ι be given.
Assume H0:
∀ x4 x5 x6 x7 . x3 (λ x8 : ι → ι → (ι → ι) → ι → ι . x8 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . setsum 0 0)) (λ x9 : ι → (ι → ι) → ι . x8 0 (x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0)) (λ x10 . 0) 0)) 0 (λ x9 . Inj1 x7) 0) (λ x8 : ι → (ι → ι) → ι . Inj0 0) = Inj1 x7.
Assume H1: ∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x3 (λ x8 : ι → ι → (ι → ι) → ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . 0) = x5.
Apply FalseE with
... ⟶ ... ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 . ...) ... ... ... = ...) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . x8) (λ x8 : (ι → ι → ι) → ι . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) (Inj1 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x9 : ι → (ι → ι) → ι . x8 (λ x10 x11 . 0)))) (λ x9 . Inj1 0)) (x5 (λ x8 . λ x9 : ι → ι . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . Inj1 (Inj0 0)) (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 . x0 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0)) (λ x11 : ι → ι → ι → ι . Inj1 0)) (x2 (λ x10 x11 . 0) (setsum 0 0)) (λ x10 . 0)) (setsum (Inj1 0) 0)) (λ x8 . x6 (λ x9 . setsum 0 (Inj0 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . 0)))) (Inj0 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . 0))))) = setsum x4 (x3 (λ x8 : ι → ι → (ι → ι) → ι → ι . x7) (λ x8 : ι → (ι → ι) → ι . 0))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x8 . Inj0 0) (λ x8 : ι → ι → ι → ι . 0) = setsum (setsum x4 (x0 (λ x8 . x8) (λ x8 : ι → ι → ι → ι . x2 (λ x9 x10 . x10) (x1 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 . 0))))) x4) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x6 x7 . x0 (λ x8 . x6) (λ x8 : ι → ι → ι → ι . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x2 (λ x10 x11 . x1 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 . λ x15 : ι → ι . x2 (λ x16 x17 . 0) 0) (λ x12 : (ι → ι → ι) → ι . setsum 0 0) (x8 0 0 0) (λ x12 . setsum 0 0)) (x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . x12) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . x10))) (λ x9 : ι → (ι → ι) → ι . 0)) = Inj1 (x3 (λ x8 : ι → ι → (ι → ι) → ι → ι . x2 (λ x9 x10 . x0 (λ x11 . x3 (λ x12 : ι → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → (ι → ι) → ι . 0)) (λ x11 : ι → ι → ι → ι . Inj0 0)) 0) (λ x8 : ι → (ι → ι) → ι . 0))) ⟶ False.