Let x0 of type (ι → (ι → ι) → ι → (ι → ι) → ι) → ι → (ι → ι) → ι be given.
Let x1 of type (ι → ι → CT2 ι) → ((CT2 ι) → ι) → ι be given.
Let x2 of type (((((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ι → CT2 ι) → ι → ι → ι be given.
Let x3 of type (ι → ι) → ι → ι be given.
Assume H0:
∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι → ι → ι . x3 (λ x8 . x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . setsum 0 0) x8 (Inj0 x6)) x4 = setsum x6 (Inj0 0).
Assume H1:
∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι → ι . x3 (λ x8 . x7 (λ x9 : (ι → ι) → ι . setsum (setsum (x0 (λ x10 . λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0) 0 (λ x10 . 0)) (Inj1 0)) (x9 (λ x10 . Inj1 0))) (Inj0 (Inj1 0))) (x0 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum 0 (setsum 0 (x0 (λ x12 . λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0) 0 (λ x12 . 0)))) (x4 (x0 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0) x5 (λ x8 . 0))) (λ x8 . x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . x9) (x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x11 0 0) (x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) 0 (λ x9 . 0)) (x1 (λ x9 x10 . λ x11 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0))) (λ x9 . 0))) = Inj1 (x1 (λ x8 x9 . λ x10 : ι → ι → ι . x7 (λ x11 : (ι → ι) → ι . x11 (λ x12 . x2 (λ x13 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0)) 0) (λ x8 : (ι → ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . x9 (λ x12 x13 . 0))))).
Assume H2:
∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x9 . λ x10 : ι → ι → ι . x10 (x0 (λ x11 . λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . setsum (setsum 0 0) x13) (x10 (x8 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) 0) (λ x11 . x1 (λ x12 x13 . λ x14 : ι → ι → ι . Inj1 0) (λ x12 : (ι → ι → ι) → ι . x9))) (x10 (x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . Inj1 0)) 0)) (x1 (λ x8 x9 . λ x10 : ι → ι → ι . x8) (λ x8 : (ι → ι → ι) → ι . x6 (x8 (λ x9 x10 . x10)))) (x3 (λ x8 . Inj0 x5) (Inj1 (x1 (λ x8 x9 . λ x10 : ι → ι → ι . x0 (λ x11 . λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0) 0 (λ x11 . 0)) (λ x8 : (ι → ι → ι) → ι . setsum 0 0)))) = Inj0 (x0 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . x12 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0)) (Inj1 (setsum 0 0)) x8) 0 (λ x8 . 0)).
Assume H3:
∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x9 . λ x10 : ι → ι → ι . Inj0 (Inj0 (setsum (x8 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (Inj1 0)))) (x3 (λ x8 . Inj0 x5) ...) ... = ....