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