Let x0 of type (ι → ι) → ι → CT3 ι be given.
Let x1 of type (ι → ι) → ι → (CT2 ι) → CT2 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 → ι) → (ι → ι → ι) → ((ι → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 : ((ι → ι) → ι) → ι . x3 (λ x8 : ι → ((ι → ι) → ι) → ι → ι → ι . x5) (λ x8 x9 . x3 (λ x10 : ι → ((ι → ι) → ι) → ι → ι → ι . x8) (λ x10 x11 . 0) (λ x10 x11 . setsum (Inj0 (Inj0 0)) (x2 (λ x12 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) 0)) (λ x10 : ι → ι . x9) (setsum (x7 (λ x10 : ι → ι . x8)) x8)) (λ x8 x9 . x3 (λ x10 : ι → ((ι → ι) → ι) → ι → ι → ι . x2 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) (x0 (λ x11 . setsum 0 0) 0 (λ x11 x12 x13 . x2 (λ x14 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x15 . 0) 0))) (λ x10 x11 . 0) (λ x10 x11 . 0) (λ x10 : ι → ι . x8) (x6 (λ x10 . 0) (setsum 0 0) (setsum x9 (Inj1 0)))) (λ x8 : ι → ι . 0) (Inj1 (x6 (λ x8 . x2 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x9 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) 0) (x7 (λ x9 : ι → ι . 0))) (x0 (λ x8 . x2 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) 0) (Inj1 0) (λ x8 x9 x10 . x1 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . 0) (λ x11 x12 . 0))) (Inj0 (Inj0 0)))) = setsum x5 0.
Assume H1:
∀ x4 x5 x6 x7 . x3 (λ x8 : ι → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x9 : ι → ((ι → ι) → ι) → ι → ι → ι . x2 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) (x1 (λ x10 . 0) x6 (λ x10 : ι → ι → ι . x1 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . 0) (λ x11 x12 . 0)) (λ x10 x11 . x3 (λ x12 : ι → ((ι → ι) → ι) → ι → ι → ι . 0) (λ x12 x13 . 0) (λ x12 x13 . 0) (λ x12 : ι → ι . 0) 0))) (λ x9 x10 . setsum 0 (Inj0 (setsum 0 0))) (λ x9 x10 . Inj0 (x8 x9 (λ x11 : ι → ι . 0) 0 (x1 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . 0) (λ x11 x12 . 0)))) (λ x9 : ι → ι . x0 (λ x10 . 0) (x3 (λ x10 : ι → ((ι → ι) → ι) → ι → ι → ι . setsum 0 0) (λ x10 x11 . 0) (λ x10 x11 . setsum 0 0) (λ x10 : ι → ι . x1 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . 0) (λ x11 x12 . 0)) 0) (λ x10 x11 x12 . x1 (λ x13 . Inj1 0) 0 (λ x13 : ι → ι → ι . x2 (λ x14 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x15 . 0) 0) (λ x13 x14 . setsum 0 0))) 0) (λ x8 x9 . 0) (λ x8 x9 . setsum (setsum x7 (setsum x6 0)) (x2 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x11 . x8) x7)) (λ x8 : ι → ι . Inj1 0) (x1 (λ x8 . 0) 0 (λ x8 : ι → ι → ι . setsum (setsum (setsum 0 0) x5) (setsum x6 0)) (λ x8 x9 . x0 (λ x10 . x7) x7 (λ x10 x11 x12 . 0))) = Inj1 (x2 (λ x8 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . λ x9 . x8 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x9) 0) ...).