Let x0 of type ((ι → ((ι → ι) → ι) → ι → ι) → ι) → ι → ι be given.
Let x1 of type (ι → ι) → ((ι → ι → ι → ι) → CT2 ι) → ι be given.
Let x2 of type (((((ι → ι) → ι → ι) → ι) → ι) → ι → ι) → ι → CT3 ι be given.
Let x3 of type ((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 : ((ι → ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι . x3 (λ x8 : ι → ι → (ι → ι) → ι → ι . x1 (λ x9 . x0 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . x10 (x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . λ x12 : ι → ι → ι . 0)) (λ x11 : ι → ι . setsum 0 0) (x2 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι . λ x12 . 0) 0 (λ x11 x12 x13 . 0))) (Inj0 (x7 0))) (λ x9 : ι → ι → ι → ι . λ x10 : ι → ι → ι . 0)) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . setsum (setsum (x3 (λ x12 : ι → ι → (ι → ι) → ι → ι . x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . λ x14 : ι → ι → ι . 0)) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 x15 . setsum 0 0)) 0) (x0 (λ x12 : ι → ((ι → ι) → ι) → ι → ι . setsum x11 0) (Inj1 (setsum 0 0)))) = x1 (λ x8 . x5 (λ x9 : ι → ι → ι . λ x10 . x2 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι . λ x12 . 0) x8 (λ x11 x12 x13 . x13))) (λ x8 : ι → ι → ι → ι . λ x9 : ι → ι → ι . setsum 0 (x6 (λ x10 . 0))).
Assume H1:
∀ x4 : ι → ι → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . x3 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj0 (x5 (λ x9 . 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . x10) = setsum (x6 (λ x8 . λ x9 : ι → ι . x2 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι . λ x11 . Inj0 (x9 0)) (Inj1 (x6 (λ x10 . λ x11 : ι → ι . 0))) (λ x10 x11 x12 . Inj0 (Inj1 0)))) 0.
Assume H2:
∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x2 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι . λ x9 . setsum (x8 (λ x10 : (ι → ι) → ι → ι . x9)) (x1 (λ x10 . x9) (λ x10 : ι → ι → ι → ι . λ x11 : ι → ι → ι . setsum 0 (x1 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . λ x13 : ι → ι → ι . 0))))) 0 (λ x8 x9 x10 . 0) = Inj1 (x2 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι . λ x9 . x0 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . 0) (x8 (λ x11 : (ι → ι) → ι → ι . 0))) 0) (x6 (λ x8 x9 . x0 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . 0) (Inj0 0)) (λ x8 : ι → ι . λ x9 . setsum 0 x7) (x4 (Inj1 0) (x0 (λ x8 : ι → ((ι → ι) → ι) → ι → ι . 0) 0))) (λ x8 x9 x10 . x10)).
Assume H3:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι . λ x9 . setsum (x2 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι . λ x11 . x10 (λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . 0) 0)) x9 (λ x10 x11 x12 . x3 (λ x13 : ι → ι → (ι → ι) → ι → ι . x2 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι . λ x15 . 0) 0 (λ x14 x15 x16 . 0)) (λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 x16 . x16))) (x1 (λ x10 . x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . λ x12 : ι → ι → ι . x10)) (λ x10 : ι → ι → ι → ι . λ x11 : ι → ι → ι . setsum (x11 0 0) (x10 0 0 0)))) (x0 (λ x8 : ι → ((ι → ι) → ι) → ι → ι . Inj0 x6) (setsum 0 (x0 (λ x8 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . 0) 0) (x2 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι . λ x9 . 0) 0 (λ x8 x9 x10 . 0))))) (λ x8 x9 x10 . x9) = Inj1 (setsum 0 0).