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