Let x0 of type ((ι → 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 be given.
Let x2 of type ((CT2 (ι → ι)) → ι) → ι → ι be given.
Let x3 of type ((CT3 ι) → ι → ((ι → ι) → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → ι → ι) → ι) → ι be given.
Assume H0:
∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . x3 (λ x8 : (ι → ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0) (λ x8 : (ι → ι → ι) → ι → ι . setsum 0 0) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι . x1 (λ x8 . x6) (λ x8 . λ x9 : ι → ι . x3 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 x14 . Inj1 0) ...) = ...) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι . x1 (λ x8 . x1 (λ x9 . x9) (λ x9 . λ x10 : ι → ι . x0 (λ x11 : ι → ι → (ι → ι) → ι . Inj0 (Inj1 0)) (λ x11 x12 x13 x14 . x12) (λ x11 x12 : ι → ι . λ x13 . setsum (x2 (λ x14 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . 0) 0) (x0 (λ x14 : ι → ι → (ι → ι) → ι . 0) (λ x14 x15 x16 x17 . 0) (λ x14 x15 : ι → ι . λ x16 . 0))))) (λ x8 . λ x9 : ι → ι . x9 (setsum (x0 (λ x10 : ι → ι → (ι → ι) → ι . x3 (λ x11 : (ι → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 x15 . 0) (λ x11 : (ι → ι → ι) → ι → ι . 0)) (λ x10 x11 x12 x13 . 0) (λ x10 x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι → (ι → ι) → ι . 0) (λ x13 x14 x15 x16 . 0) (λ x13 x14 : ι → ι . λ x15 . 0))) (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . 0) (Inj1 0)))) = Inj0 (Inj1 (x3 (λ x8 : (ι → ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0) (λ x8 : (ι → ι → ι) → ι → ι . x1 (λ x9 . 0) (λ x9 . λ x10 : ι → ι . x0 (λ x11 : ι → ι → (ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 : ι → ι . λ x13 . 0)))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι . setsum (x7 (Inj1 (x7 0 (λ x9 x10 . 0))) (λ x9 x10 . x3 (λ x11 : (ι → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 x15 . x15) (λ x11 : (ι → ι → ι) → ι → ι . Inj1 0))) (Inj1 (x0 (λ x9 : ι → ι → (ι → ι) → ι . x7 0 (λ x10 x11 . 0)) (λ x9 x10 x11 x12 . x11) (λ x9 x10 : ι → ι . λ x11 . Inj0 0)))) (λ x8 x9 x10 x11 . Inj1 (Inj1 0)) (λ x8 x9 : ι → ι . λ x10 . x3 (λ x11 : (ι → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 x15 . Inj1 (x0 (λ x16 : ι → ι → (ι → ι) → ι . 0) (λ x16 x17 x18 x19 . Inj1 0) (λ x16 x17 : ι → ι . λ x18 . setsum 0 0))) (λ x11 : (ι → ι → ι) → ι → ι . Inj1 (x0 (λ x12 : ι → ι → (ι → ι) → ι . x9 0) (λ x12 x13 x14 x15 . 0) (λ x12 x13 : ι → ι . λ x14 . 0)))) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι . x8 (x8 (x1 (λ x9 . setsum 0 0) (λ x9 . λ x10 : ι → ι . setsum 0 0)) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . 0) 0) (λ x9 . x0 (λ x10 : ι → ι → (ι → ι) → ι . x0 (λ x11 : ι → ι → (ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 : ι → ι . λ x13 . 0)) (λ x10 x11 x12 x13 . x12) (λ x10 x11 : ι → ι . λ x12 . 0))) 0 (λ x9 . 0)) (λ x8 x9 x10 x11 . 0) (λ x8 x9 : ι → ι . λ x10 . x7 (x0 (λ x11 : ι → ι → (ι → ι) → ι . x10) (λ x11 x12 x13 x14 . x14) (λ x11 x12 : ι → ι . λ x13 . 0)) (x1 (λ x11 . x2 (λ x12 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . x10) x11) (λ x11 . λ x12 : ι → ι . x11))) = Inj0 x5) ⟶ False.