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