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