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