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