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) → ι be given.
Let x2 of type (ι → ι) → (ι → CT2 ι) → ι be given.
Let x3 of type (((ι → ι → ι) → ι → ι → ι → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 x7 . x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . 0) (x1 (λ x8 : ι → ι . 0) (Inj0 (x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . x1 (λ x9 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . 0)) 0)) (λ x8 . λ x9 : ι → ι . Inj0 0)) = setsum (Inj1 (Inj1 0)) (x5 x6 (Inj1 (setsum (x1 (λ x8 : ι → ι . 0) 0 (λ x8 . λ x9 : ι → ι . 0)) (setsum 0 0))) (x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . setsum x7 (x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . 0))) (Inj0 (x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . 0) (λ x8 x9 . 0))))).
Assume H1:
∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . setsum (x10 0 0) (setsum (x10 0 0) (x8 (λ x11 x12 . 0) 0 0 0)))) x7 = Inj0 (Inj1 0).
Assume H2: ∀ x4 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 . x8) (λ x8 . λ x9 : ι → ι → ι . 0) = x7.
Apply FalseE with
... ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . x1 (λ x8 : ι → ι . 0) 0 (λ x8 . λ x9 : ι → ι . x6 (x9 0)) = x6 (x6 (x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . ...) ...))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι . x1 (λ x8 : ι → ι . 0) 0 (λ x8 . λ x9 : ι → ι . Inj1 (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 : ι → ι . x13 (x0 (λ x14 x15 . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) (λ x14 x15 . 0))) (λ x10 x11 . Inj0 (x3 (λ x12 : (ι → ι → ι) → ι → ι → ι → ι . 0) 0)))) = setsum 0 (Inj1 (x5 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . setsum 0 (Inj1 (Inj1 (x10 0 0)))) (λ x8 x9 . 0) = x7 (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . x11 (Inj1 (x10 x9 (x11 0)))) (λ x8 x9 . 0) = setsum (x4 (λ x8 . λ x9 : ι → ι . λ x10 . x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . x0 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) (λ x12 x13 . Inj0 0)) 0)) (setsum (x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . x2 (λ x9 . x8 (λ x10 x11 . 0) 0 0 0) (λ x9 . λ x10 : ι → ι → ι . x2 (λ x11 . 0) (λ x11 . λ x12 : ι → ι → ι . 0))) (x2 (λ x8 . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 x10 . 0)) (λ x8 . λ x9 : ι → ι → ι . x7 0 (λ x10 x11 . 0) 0))) (Inj0 (x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . x11 0) (λ x8 x9 . 0))))) ⟶ False.