Let x0 of type (ι → ι → ι) → CT3 ι be given.
Let x1 of type (ι → ι) → ι → ι → ι be given.
Let x2 of type (ι → ι → ι) → ι → ι be given.
Let x3 of type (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → ι be given.
Assume H0: ∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 : (ι → (ι → ι) → ι → ι) → ι . x7) x4 = x7.
Assume H1:
∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x8 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x9 x10 . x1 (λ x11 . x3 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum 0 0)) 0 (x8 (λ x11 . λ x12 : ι → ι . λ x13 . x12 0))) (λ x9 x10 x11 . x11)) (setsum 0 0) = setsum x7 (x1 (λ x8 . x0 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) x7) (λ x9 x10 x11 . x9)) (x1 (λ x8 . x6) x5 (setsum (Inj1 0) x7)) (setsum x7 (x1 (λ x8 . 0) (x4 0) x7))).
Assume H2:
∀ x4 : ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x2 (λ x8 x9 . x2 (λ x10 x11 . setsum (Inj0 0) 0) 0) 0 = x2 (λ x8 x9 . Inj1 0) (setsum x6 (x4 x6 0 (x3 (λ x8 : (ι → (ι → ι) → ι → ι) → ι . 0) x6))).
Assume H3:
∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 x9 . x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x10 x11 . x0 (λ x12 x13 . x1 (λ x14 . 0) 0 0) (λ x12 x13 x14 . Inj1 0)) (λ x10 x11 x12 . setsum x9 x11))) (Inj0 0) = setsum 0 (setsum 0 0).
Assume H4:
∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x1 (λ x8 . x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (Inj1 (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x6) 0))) (x1 (λ x8 . Inj0 (setsum (Inj0 0) (x2 (λ x9 x10 . 0) 0))) x5 (Inj0 (Inj1 0))) (x0 (λ x8 x9 . 0) (λ x8 x9 x10 . x8)) = setsum x6 (setsum (x0 (λ x8 x9 . Inj0 (setsum 0 0)) (λ x8 x9 x10 . x7 (λ x11 . x9) (λ x11 : ι → ι . x8) x8 (x1 (λ x11 . 0) 0 0))) (x0 (λ x8 x9 . x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x11 x12 . 0) 0) (setsum 0 0)) (λ x8 x9 x10 . 0))).
Assume H5:
∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x8 . 0) (x3 (λ x8 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum (x2 (λ x8 x9 . x8) 0) 0)) 0 = x3 (λ x8 : (ι → (ι → ι) → ι → ι) → ι . setsum (Inj0 (setsum x6 x6)) (setsum (x5 (λ x9 x10 x11 . x0 (λ x12 x13 . 0) (λ x12 x13 x14 . 0))) (setsum (x5 (λ x9 x10 x11 . 0)) 0))) (x0 (λ x8 x9 . x0 (λ x10 x11 . setsum (x1 (λ x12 . 0) 0 0) 0) (λ x10 x11 x12 . x11)) (λ x8 x9 x10 . setsum x8 (Inj1 (x2 (λ x11 x12 . 0) 0)))).