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