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