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) → ((CT2 ι) → ι) → ι be given.
Let x2 of type (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 be given.
Assume H0:
∀ x4 x5 x6 x7 . x3 (λ x8 . setsum (x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . 0)) x6) (x2 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι → ι → ι . λ x9 x10 : ι → ι . λ x11 . x2 (λ x12 . x1 (λ x13 x14 . x0 (λ x15 x16 . 0) (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0)) (λ x13 : (ι → ι → ι) → ι . 0)) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . x13 (x14 0)))) = Inj1 (setsum x5 0).
Assume H1:
∀ x4 x5 x6 x7 . x3 (λ x8 . Inj1 (x2 (λ x9 . Inj0 (x0 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . 0))) (setsum (x1 (λ x8 x9 . x3 (λ x10 . x7) x9) (λ x8 : (ι → ι → ι) → ι . x0 (λ x9 x10 . setsum 0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0))) x5) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → ι → ι → ι . x0 (λ x8 x9 . 0) (λ x8 x9 . λ x10 : ι → ι . λ x11 . Inj0 (setsum (setsum x11 (x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0))) (setsum 0 (x0 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0))))) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0) = setsum (x3 (λ x8 . x5) 0) (x0 ... ... ...)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . x1 (λ x10 x11 . x1 (λ x12 x13 . Inj1 x10) (λ x12 : (ι → ι → ι) → ι . Inj0 (x1 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . 0)))) (λ x10 : (ι → ι → ι) → ι . x9)) (λ x8 x9 . λ x10 : ι → ι . λ x11 . Inj0 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . x2 (λ x11 . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . λ x12 x13 : ι → ι . λ x14 . 0)) = x1 (λ x8 x9 . x0 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . x3 (λ x14 . x2 (λ x15 . 0) (λ x15 : (ι → ι → ι) → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . 0)) x12) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x1 (λ x17 x18 . 0) (λ x17 : (ι → ι → ι) → ι . x1 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → ι . 0))))) (λ x8 : (ι → ι → ι) → ι . x0 (λ x9 x10 . x1 (λ x11 x12 . x0 (λ x13 x14 . x0 (λ x15 x16 . 0) (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0)) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x3 (λ x16 . 0) 0)) (λ x11 : (ι → ι → ι) → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x11 (x11 (x11 0))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0))) ⟶ False.