Let x0 of type ((CT2 ι) → ι) → ((ι → ι) → ι → ι → ι → ι) → ι be given.
Let x1 of type (ι → ι) → ι → ι be given.
Let x2 of type (ι → ((ι → ι) → ι → ι) → ι) → 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) → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . x3 (λ x8 . setsum x8 (x1 (λ x9 . 0) 0)) (x0 (λ x8 : (ι → ι → ι) → ι . x0 (λ x9 : (ι → ι → ι) → ι . x2 (λ x10 . λ x11 : (ι → ι) → ι → ι . x10) (x1 (λ x10 . 0) 0) (λ x10 . Inj0 0)) (λ x9 : ι → ι . λ x10 x11 x12 . 0)) (λ x8 : ι → ι . λ x9 x10 x11 . x8 (Inj1 x11))) = Inj0 (x0 (λ x8 : (ι → ι → ι) → ι . Inj1 (x0 (λ x9 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 x11 x12 . x9 0))) (λ x8 : ι → ι . λ x9 x10 x11 . 0)).
Assume H1:
∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . setsum 0 (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι . x2 (λ x11 . λ x12 : (ι → ι) → ι → ι . x2 (λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x13 . 0)) (Inj1 0) (λ x11 . x0 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 x14 x15 . 0))) x7 (λ x9 . x6 0))) (setsum (x3 (λ x8 . setsum x7 x8) x7) (setsum (x2 (λ x8 . λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0) (x4 (λ x8 : (ι → ι) → ι → ι . λ x9 . 0) (λ x8 : ι → ι . 0)) (λ x8 . x7)) (x1 (λ x8 . setsum 0 0) 0))) = setsum (x0 (λ x8 : (ι → ι → ι) → ι . x3 (λ x9 . x3 (λ x10 . x1 (λ x11 . 0) 0) (x6 0)) 0) (λ x8 : ι → ι . λ x9 x10 x11 . Inj0 0)) x7.
Assume H2:
∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x8 . λ x9 : (ι → ι) → ι → ι . Inj1 0) (setsum x5 (Inj1 x5)) (λ x8 . Inj1 x8) = Inj1 (x3 (λ x8 . 0) (x2 (λ x8 . λ x9 : (ι → ι) → ι → ι . x2 (λ x10 . λ x11 : (ι → ι) → ι → ι . 0) x6 (λ x10 . x10)) 0 (λ x8 . x8))).
Assume H3:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : (ι → ι) → ι → ι . Inj1 (setsum (x9 (λ x10 . x3 (λ x11 . 0) 0) 0) (setsum (x9 (λ x10 . 0) 0) (x3 (λ x10 . 0) 0)))) (x7 0) (λ x8 . Inj0 (setsum 0 (Inj1 (setsum 0 0)))) = x7 (Inj1 (x5 0)).
Assume H4:
∀ x4 x5 x6 x7 . x1 (λ x8 . x5) x6 = Inj0 0.
Assume H5:
∀ x4 x5 x6 x7 . x1 (λ x8 . setsum 0 (setsum (x1 (λ x9 . x2 (λ x10 . λ x11 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0)) 0) (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι . x3 (λ x11 . 0) 0) (setsum 0 0) (λ x9 . x0 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))))) 0 = x7.