Let x0 of type ((ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι be given.
Let x1 of type (ι → ι) → ι → ι → CN (ι → ι) be given.
Let x2 of type (ι → ι → ι → ι) → ((CT2 ι) → ι) → ι be given.
Let x3 of type (((CT2 ι) → ι → ι → ι) → ι) → ((ι → ι) → ι → (ι → ι) → ι → ι) → ι be given.
Assume H0: ∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x8 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . λ x11 . x10 (x10 (x2 (λ x12 x13 x14 . x3 (λ x15 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0)) (λ x12 : (ι → ι → ι) → ι . 0)))) = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι → ι . x0 (λ x8 : ι → ι . setsum (x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . setsum (x9 (λ x10 : ι → ι → ι . 0) 0 0) (x6 (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0) 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x2 (λ x9 x10 x11 . x9) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 . x10) (setsum 0 0) (setsum 0 0) (λ x10 : ι → ι . λ x11 . x0 (λ x12 : ι → ι . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x10 . 0) (x9 (λ x10 x11 . 0))))) (λ x8 : ι → (ι → ι) → ι . λ x9 . λ x10 : ι → ι . λ x11 . Inj1 (Inj1 (Inj0 (setsum 0 0)))) = x6 (λ x8 . x8) (λ x8 : ι → ι . λ x9 . x2 (λ x10 x11 x12 . x3 (λ x13 : ((ι → ι → ι) → ι) → ι → ι → ι . x10) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 . x16) (x0 (λ x17 : ι → ι . 0) (λ x17 : ι → (ι → ι) → ι . λ x18 . λ x19 : ι → ι . λ x20 . 0)) (x15 0) (λ x17 : ι → ι . λ x18 . setsum 0 0) (λ x17 . x0 (λ x18 : ι → ι . 0) (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 . 0)) x16)) (λ x10 : (ι → ι → ι) → ι . x2 (λ x11 x12 x13 . x3 (λ x14 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x15 : ι → ι . 0) (λ x15 : ι → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0)) ...) ...)) ... ...) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → ι . x0 (λ x8 : ι → ι . x8 0) (λ x8 : ι → (ι → ι) → ι . λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ((ι → ι → ι) → ι) → ι → ι → ι . Inj1 (x12 (λ x13 : ι → ι → ι . setsum 0 0) (x10 0) 0)) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . x15)) = x3 (λ x8 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . Inj0 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x11 (setsum (setsum 0 0) (Inj0 0)))) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 . Inj1 x9) 0 (setsum (setsum (Inj1 0) (x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0)) 0) (λ x12 : ι → ι . λ x13 . x3 (λ x14 : ((ι → ι → ι) → ι) → ι → ι → ι . setsum (x2 (λ x15 x16 x17 . 0) (λ x15 : (ι → ι → ι) → ι . 0)) (x2 (λ x15 x16 x17 . 0) (λ x15 : (ι → ι → ι) → ι . 0))) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . x3 (λ x18 : ((ι → ι → ι) → ι) → ι → ι → ι . x17) (λ x18 : ι → ι . λ x19 . λ x20 : ι → ι . λ x21 . Inj0 0))) (λ x12 . setsum 0 x9) (Inj1 0))) ⟶ False.