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