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