Let x0 of type (ι → ι → (ι → ι → ι) → ι → ι) → ι → ((ι → ι) → ι) → ι be given.
Let x1 of type (ι → ι → CN (ι → ι)) → ι → ι be given.
Let x2 of type (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 be given.
Assume H0:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι → ι . setsum x7 0) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0) (x0 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 . 0) x11 (λ x12 : ι → ι . x10 0 0))) (x2 (λ x8 . x3 (λ x9 : ι → ι . x9 x8) (λ x9 : ι → (ι → ι) → ι → ι . x3 (λ x10 : ι → ι . x7 0 0 0) (λ x10 : ι → (ι → ι) → ι → ι . x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x11 : ι → ι . 0)))) (λ x8 : ι → ι . Inj1 (x8 (Inj0 0))) (λ x8 x9 . x7 x9 (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 . x10) (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 . 0) 0 (λ x10 : ι → ι . 0)) (λ x10 : ι → ι . setsum 0 0)) 0) (λ x8 x9 . 0) (Inj1 (x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 . Inj1 0) 0 (λ x8 : ι → ι . x8 0)))) (λ x8 : ι → ι . x5) = x1 (λ x8 x9 . ...) ...) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 . x0 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 . x2 (λ x16 . x2 (λ x17 . x14 0 0) (λ x17 : ι → ι . setsum 0 0) (λ x17 x18 . x3 (λ x19 : ι → ι . 0) (λ x19 : ι → (ι → ι) → ι → ι . 0)) (λ x17 x18 . 0) 0) (λ x16 : ι → ι . Inj1 (setsum 0 0)) (λ x16 x17 . x14 x17 (x1 (λ x18 x19 . λ x20 : (ι → ι) → ι → ι . λ x21 : ι → ι . λ x22 . 0) 0)) (λ x16 x17 . x3 (λ x18 : ι → ι . x3 (λ x19 : ι → ι . 0) (λ x19 : ι → (ι → ι) → ι → ι . 0)) (λ x18 : ι → (ι → ι) → ι → ι . x2 (λ x19 . 0) (λ x19 : ι → ι . 0) (λ x19 x20 . 0) (λ x19 x20 . 0) 0)) 0) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . x14 (λ x17 . setsum 0 0) 0) x9) (λ x12 : ι → ι . setsum (x2 (λ x13 . x12 0) (λ x13 : ι → ι . x0 (λ x14 x15 . λ x16 : ι → ι → ι . λ x17 . 0) 0 (λ x14 : ι → ι . 0)) (λ x13 x14 . 0) (λ x13 x14 . x14) x11) (Inj0 x11))) (setsum 0 0) (λ x8 : ι → ι . x6) = x0 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 . Inj1 (setsum (Inj1 (x3 (λ x12 : ι → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0))) x11)) (setsum (Inj0 0) 0) (λ x8 : ι → ι . setsum (x7 (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (setsum 0 0)) (λ x9 . x3 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι → ι . x1 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0))) (setsum x6 x5))) ⟶ False.