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