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