Let x0 of type (ι → (ι → ι) → ι) → ι → ι → (ι → ι) → ι be given.
Let x1 of type (ι → ι) → (CT2 ι) → ι be given.
Let x2 of type (ι → ι → (ι → ι → ι) → (ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι) → ι be given.
Let x3 of type (ι → ι) → ((ι → ι) → CT2 ι) → ι → ι be given.
Assume H0:
∀ x4 : (ι → ι) → ι → ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x3 (λ x8 . 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . 0) (x7 (λ x8 : ι → ι → ι . setsum (x8 0 (x7 (λ x9 : ι → ι → ι . 0))) (x7 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) (λ x10 . 0) (λ x10 : ι → ι . 0))))) = x7 (λ x8 : ι → ι → ι . setsum (Inj0 (x7 (λ x9 : ι → ι → ι . setsum 0 0))) (x3 (λ x9 . x7 (λ x10 : ι → ι → ι . 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) (x8 (Inj0 0) (setsum 0 0)))).
Assume H1: ∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 . x7) (λ x8 : ι → ι . λ x9 : ι → ι → ι . x8 x6) x7 = x7.
Assume H2:
∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . 0) (λ x8 . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x8) x8) (λ x8 : ι → ι . setsum (x0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x0 (λ x12 . λ x13 : ι → ι . 0) 0 0 (λ x12 . 0)) (λ x11 : ι → ι . λ x12 : ι → ι → ι . setsum 0 0) (Inj0 0)) (x0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 : ι → ι → ι . 0) 0) 0 (Inj1 0) (λ x9 . Inj1 0)) (Inj1 (setsum 0 0)) (λ x9 . x9)) 0) = setsum x5 0.
Assume H3:
∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . 0) (λ x8 . x1 (λ x9 . x9) (λ x9 : ι → ι → ι . x9 0 (x9 (x1 (λ x10 . 0) (λ x10 : ι → ι → ι . 0)) x7))) (λ x8 : ι → ι . x8 (x1 (λ x9 . 0) (λ x9 : ι → ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . x1 (λ x12 . 0) (λ x12 : ι → ι → ι . 0))))) = setsum (x2 (λ x8 x9 . λ x10 : ι → ι → ι . λ x11 : ι → ι . setsum 0 (setsum (x10 0 0) x8)) (λ x8 . x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x9 (λ x11 . 0) 0) 0)) (λ x8 : ι → ι . x7)) (x1 (λ x8 . setsum x7 0) (λ x8 : ι → ι → ι . x8 (x8 (Inj1 0) 0) (x1 (λ x9 . x7) (λ x9 : ι → ι → ι . x9 0 0)))).
Assume H4:
∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 . setsum 0 (Inj0 (x6 (λ x9 : ι → ι . x6 (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0) (Inj1 0) (λ x9 . x9) x7))) (λ x8 : ι → ι → ι . 0) = x4 (x6 (λ x8 : ι → ι . x8 (setsum 0 0)) x5 (λ x8 . x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 . ...) ...) ...).