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 → ι) → ι) → ι) → ι be given.
Let x2 of type (((((ι → ι) → ι → 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) → ι → ι → ι) → ι be given.
Assume H0:
∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x7 : ι → ι → ι . x3 (λ x8 : ι → ι . x7 (x7 (x5 (λ x9 . x1 (λ x10 . 0) (λ x10 : ι → (ι → ι) → ι . 0)) (x6 (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0 0 0) (λ x9 . x1 (λ x10 . 0) (λ x10 : ι → (ι → ι) → ι . 0))) (x6 (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 0) 0 (x6 (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0 0 0) (setsum 0 0))) (setsum (setsum (x5 (λ x9 . 0) 0 (λ x9 . 0)) 0) 0)) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . 0) = x7 (x2 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . setsum (Inj0 (x7 0 0)) (Inj1 (x7 0 0))) (λ x8 . 0)) (x3 (λ x8 : ι → ι . x3 (λ x9 : ι → ι . x2 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x2 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0)) (λ x10 . x10)) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x2 (λ x13 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 . 0)) (Inj1 0))) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . 0)).
Assume H1:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι . x8 (Inj1 (x0 (λ x9 . x1 (λ x10 . 0) (λ x10 : ι → (ι → ι) → ι . 0)) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . Inj1 0) (x3 (λ x9 : ι → ι . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . 0))))) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . x1 (λ x12 . x11) (λ x12 : ι → (ι → ι) → ι . x3 (λ x13 : ι → ι . x13 (x1 (λ x14 . 0) (λ x14 : ι → (ι → ι) → ι . 0))) (λ x13 : ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . x14 0 0))) = Inj1 (x2 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x7) (λ x8 . 0)).
Assume H2:
∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x2 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x6) (λ x8 . setsum 0 x6) = Inj0 0.
Assume H3:
∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x1 (λ x9 . 0) (λ x9 : ι → (ι → ι) → ι . x8 (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum x11 (x3 (λ x12 : ι → ι . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . 0))) (λ x10 . 0) (λ x10 . 0) (x7 (λ x10 : ι → ι → ι . x0 (λ x11 . 0) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) 0)))) (λ x8 . 0) = setsum (x6 (λ x8 . 0)) x4.
Assume H4:
∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x8 . Inj1 x5) (λ x8 : ι → (ι → ι) → ι . x7) = Inj0 x6.
Assume H5:
∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x1 (λ x8 . Inj0 x8) (λ x8 : ι → (ι → ι) → ι . setsum (x7 0 (x5 0 (λ x9 : ι → ι . Inj0 0) (Inj0 0)) (λ x9 . x8 (x7 0 0 ... 0) ...) ...) 0) = ....