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