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