Let x0 of type (ι → ι) → (((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 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 → ι) → ι → ι) → (ι → ι) → ι → ι be given.
Assume H0: ∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x8 : ι → ((ι → ι) → ι) → ι → ι → ι . λ x9 . 0) (λ x8 . 0) 0 = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 x6 x7 . x1 (λ x8 . 0) (λ x8 : ι → ι . x3 (λ x9 : ι → ((ι → ι) → ι) → ι → ι → ι . λ x10 . x0 (λ x11 . x9 (Inj1 0) (λ x12 : ι → ι . 0) (Inj1 0) (setsum 0 0)) (λ x11 : (ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 x14 . Inj0 (x12 (λ x15 . 0)))) (λ x9 . setsum (Inj1 (x3 (λ x10 : ι → ((ι → ι) → ι) → ι → ι → ι . λ x11 . 0) (λ x10 . 0) 0)) (setsum (x2 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . λ x13 x14 . 0) 0) (setsum 0 0))) 0) = ...) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 . x1 (λ x8 . x0 (λ x9 . x1 (λ x10 . x9) (λ x10 : ι → ι . Inj0 0)) (λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 x12 . 0)) (λ x8 : ι → ι . Inj0 (x6 (λ x9 : ι → ι . x3 (λ x10 : ι → ((ι → ι) → ι) → ι → ι → ι . λ x11 . x0 (λ x12 . 0) (λ x12 : (ι → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . λ x14 x15 . 0)) (λ x10 . x3 (λ x11 : ι → ((ι → ι) → ι) → ι → ι → ι . λ x12 . 0) (λ x11 . 0) 0) (x6 (λ x10 : ι → ι . 0))))) = setsum (x0 (λ x8 . Inj0 (x6 (λ x9 : ι → ι . x7))) (λ x8 : (ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 x11 . 0)) 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x8 . 0) (λ x8 : (ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 x11 . x1 (λ x12 . setsum (x9 (λ x13 . x10)) (setsum x10 (Inj0 0))) (λ x12 : ι → ι . setsum (x1 (λ x13 . 0) (λ x13 : ι → ι . x2 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι → ι . λ x17 x18 . 0) 0)) (setsum (Inj1 0) (x3 (λ x13 : ι → ((ι → ι) → ι) → ι → ι → ι . λ x14 . 0) (λ x13 . 0) 0)))) = x1 (λ x8 . x6) (λ x8 : ι → ι . x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum (x0 (λ x11 . x8 0) (λ x11 : (ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 x14 . Inj1 0)) (setsum 0 0)) (λ x9 : ι → ι . x7 (x8 (x7 0 0)) (x9 (x1 (λ x10 . 0) (λ x10 : ι → ι . 0)))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 . Inj1 (x5 (x0 (λ x9 . setsum 0 0) (λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 x12 . 0)))) (λ x8 : (ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 x11 . 0) = setsum (setsum x7 0) (x0 (λ x8 . x2 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 x13 . x13) (x1 (λ x9 . x6) (λ x9 : ι → ι . 0))) (λ x8 : (ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 x11 . x0 (λ x12 . setsum 0 (x9 (λ x13 . 0))) (λ x12 : (ι → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . λ x14 x15 . x2 (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . λ x19 x20 . 0) 0)))) ⟶ False.