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 → ι) → ι → ι be given.
Let x2 of type (((ι → ι) → ι) → ι) → CT2 ι be given.
Let x3 of type (((((ι → ι) → ι) → (ι → ι) → ι) → ι) → ι) → (ι → ι → (ι → ι) → ι → ι) → ι be given.
Assume H0:
∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → (ι → ι) → ι . x3 (λ x8 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . x7 (λ x9 . 0) (λ x9 . 0)) (λ x8 x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι . λ x13 . x13) (x0 (λ x12 : (ι → ι) → ι . 0) (λ x12 . Inj0 (setsum 0 0))) 0 (x3 (λ x12 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . x2 (λ x13 : (ι → ι) → ι . x12 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (λ x13 x14 . x3 (λ x15 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . 0) (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0))) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x1 (λ x16 : (((ι → ι) → ι → ι) → ι) → ι . λ x17 . x1 (λ x18 : (((ι → ι) → ι → ι) → ι) → ι . λ x19 . 0) 0 0 0 (λ x18 . 0) 0) x12 x13 (x0 (λ x16 : (ι → ι) → ι . 0) (λ x16 . 0)) (λ x16 . x13) x15)) (λ x12 . 0) (x0 (λ x12 : (ι → ι) → ι . 0) (λ x12 . x11))) = setsum (x5 0 (x5 (Inj0 (x0 (λ x8 : (ι → ι) → ι . 0) (λ x8 . 0))) 0)) (setsum (x2 (λ x8 : (ι → ι) → ι . 0) (λ x8 x9 . setsum 0 x8)) (setsum (x7 (λ x8 . x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0)) (λ x8 . Inj0 0)) (setsum 0 x4))).
Assume H1:
∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x6 : (ι → ι → ι) → (ι → ι → ι) → ι . ∀ x7 : ι → ι . x3 (λ x8 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . 0) (λ x8 x9 . λ x10 : ι → ι . λ x11 . 0) = setsum (x7 (Inj1 (x0 (λ x8 : (ι → ι) → ι . Inj0 0) (λ x8 . x8)))) (setsum (Inj0 (x2 (λ x8 : (ι → ι) → ι . 0) (λ x8 x9 . Inj1 0))) (x4 (λ x8 . setsum (x6 (λ x9 x10 . 0) (λ x9 x10 . 0)) 0) (λ x8 : ι → ι . λ x9 . Inj1 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι . λ x11 . 0) 0 0 0 (λ x10 . 0) 0)))).
Assume H2:
∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x8 : (ι → ι) → ι . 0) (λ x8 x9 . x7 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι . λ x11 . 0) (x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . Inj1 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 0)) 0 x8 (λ x10 . 0) (setsum (setsum 0 0) 0))) = Inj0 (setsum x5 (x2 (λ x8 : (ι → ι) → ι . x5) (λ x8 x9 . x9))).
Assume H3:
∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 : (ι → ι) → ι . 0) (λ x8 x9 . Inj0 0) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x8 : (ι → ι) → ι . Inj0 (x8 (λ x9 . 0))) (λ x8 . x7 (Inj0 0) (λ x9 : ι → ι . x7 0 (λ x10 : ι → ι . x8))) = x7 (Inj0 (Inj1 (setsum 0 (x0 (λ x8 : (ι → ι) → ι . 0) (λ x8 . 0))))) (λ x8 : ι → ι . Inj0 (x7 (setsum (x8 0) (Inj0 0)) (λ x9 : ι → ι . ...)))) ⟶ False.