Let x0 of type (ι → ι) → ι → (((ι → ι) → ι → ι) → ι) → CT2 ι be given.
Let x1 of type ((((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 be given.
Let x3 of type (ι → ι) → ι → ι be given.
Assume H0:
∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x3 (λ x8 . x1 (λ x9 : ((ι → ι) → ι) → ι . 0) (λ x9 . x0 (λ x10 . x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . Inj1 0) (setsum 0 0)) x9 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 x11 . 0))) (Inj1 (setsum 0 (x0 (λ x8 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) 0) x6 (λ x8 : (ι → ι) → ι → ι . 0) (λ x8 x9 . 0)))) = Inj0 (setsum (setsum (x2 (λ x8 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) 0) (Inj1 0)) x6) (x3 (λ x8 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) x6) (x2 (λ x8 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x9 . 0) (setsum 0 0)))).
Assume H1:
∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x8 . Inj0 (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ((ι → ι) → ι) → ι . 0) (λ x11 . x0 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0))) x8)) 0 = x5 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . setsum 0 0) x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x1 (λ x8 : ((ι → ι) → ι) → ι . Inj0 (Inj1 0)) (λ x8 . x3 (λ x9 . ...) ...) = ...) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x0 (λ x8 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x3 (λ x11 . x9 (λ x12 : ι → ι . λ x13 x14 . setsum 0 0) 0) (Inj1 0)) x8) 0 (λ x8 : (ι → ι) → ι → ι . x5) (λ x8 x9 . setsum (x0 (λ x10 . setsum (x1 (λ x11 : ((ι → ι) → ι) → ι . 0) (λ x11 . 0)) (x0 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0))) (x1 (λ x10 : ((ι → ι) → ι) → ι . x10 (λ x11 : ι → ι . 0)) (λ x10 . Inj1 0)) (λ x10 : (ι → ι) → ι → ι . setsum 0 (x7 0 (λ x11 : ι → ι . 0) (λ x11 . 0))) (λ x10 x11 . 0)) (x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . x11) (Inj1 (setsum 0 0)))) = Inj0 (Inj1 (x4 (x0 (λ x8 . x7 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) 0 (λ x8 : (ι → ι) → ι → ι . Inj1 0) (λ x8 x9 . x8)) (Inj0 x5)))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x0 (λ x8 . setsum x7 0) (x3 (λ x8 . 0) x7) (λ x8 : (ι → ι) → ι → ι . x7) (λ x8 x9 . 0) = x3 (λ x8 . x1 (λ x9 : ((ι → ι) → ι) → ι . x9 (λ x10 : ι → ι . 0)) (λ x9 . x8)) (setsum (x2 (λ x8 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x9 . setsum 0 (x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) 0)) (Inj0 (setsum 0 0))) (setsum x5 (setsum (Inj0 0) 0)))) ⟶ False.