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