Let x0 of type (((ι → (ι → 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 → ((ι → ι) → ι) → ι → ι → ι) → (ι → ι) → ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι → ι → ι be given.
Let x2 of type ((((ι → ι) → ι) → ι → ι → ι) → ι → CN (ι → ι)) → ι → ι be given.
Let x3 of type (ι → ι) → ι → (CT2 ι) → (ι → ι) → ι be given.
Assume H0:
∀ x4 x5 x6 x7 . x3 (λ x8 . 0) 0 (λ x8 : ι → ι → ι . Inj0 (Inj0 (Inj1 0))) (λ x8 . x8) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 . x0 (λ x8 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x9 x10 . setsum x7 (x2 (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . x0 (λ x16 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x17 x18 . Inj1 0) (λ x16 . Inj1 0)) (Inj0 (Inj1 0)))) (λ x8 . x3 (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 x12 . 0) (λ x10 . setsum (Inj0 0) x10)) (Inj0 (setsum x7 (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x9 . 0) (λ x9 : ι → ι → ι . λ x10 x11 . 0) (λ x9 : ι → ι . 0) 0 0))) (λ x9 : ι → ι → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x14 x15 . x14) (λ x13 . 0)) (λ x10 . x10)) (λ x9 . x8)) = x3 (λ x8 . x6 (λ x9 . λ x10 : ι → ι . x8) x8 (x6 (λ x9 . λ x10 : ι → ι . 0) (x6 (λ x9 . λ x10 : ι → ι . x10 0) (Inj1 0) (setsum 0 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . 0) (λ x9 . 0))) (x3 (λ x9 . 0) x7 (λ x9 : ι → ι → ι . setsum 0 0) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x10 . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x10 : ι → ι . 0) 0 0)) (x6 (λ x9 . λ x10 : ι → ι . setsum 0 0) 0 (Inj1 0) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x9 . 0) (λ x9 : ι → ι → ι . λ x10 x11 . 0) (λ x9 : ι → ι . 0) 0 0))) 0) (x6 (λ x8 . λ x9 : ι → ι . x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 (setsum 0 0)) x8) (x3 (λ x8 . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x9 . x8) (λ x9 : ι → ι → ι . λ x10 x11 . Inj0 0) (λ x9 : ι → ι . x8) (x2 (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0) 0) (x5 (λ x8 x9 x10 . setsum 0 0)) (λ x8 : ι → ι → ι . x8 (Inj0 0) (x6 (λ x9 . λ x10 : ι → ι . 0) 0 0 0)) (λ x8 . x6 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . 0) (λ x11 . 0)) 0 x7 (Inj1 0))) (x5 (λ x8 x9 x10 . Inj0 0)) x7) (λ x8 : ι → ι → ι . Inj0 (x5 (λ x9 x10 x11 . setsum (Inj1 0) (Inj0 0)))) (λ x8 . x3 (λ x9 . ...) ... ... ...)) ⟶ False.