Let x0 of type (ι → ι → 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 be given.
Let x2 of type ((ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → ((CT2 ι) → ι) → ι → ι → ι be given.
Let x3 of type (ι → (((ι → ι) → ι) → ι) → ι → ι) → (((ι → ι) → ι → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x8 . λ x9 : ((ι → ι) → ι) → ι . λ x10 . x9 (λ x11 : ι → ι . 0)) (λ x8 : (ι → ι) → ι → ι . 0) (Inj0 (setsum (x0 (λ x8 x9 x10 . 0) (x4 0)) 0)) = setsum (x7 (λ x8 : ι → ι . Inj1 (x0 (λ x9 x10 x11 . x10) (setsum 0 0))) (λ x8 : ι → ι . λ x9 . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . Inj0 (setsum 0 0)) (λ x10 : (ι → ι) → ι → ι . 0) (x0 (λ x10 x11 x12 . x10) 0)) (λ x8 . x7 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . Inj0 (Inj0 0)) (λ x9 . x0 (λ x10 x11 x12 . setsum 0 0) 0) 0) (x7 (λ x8 : ι → ι . 0) (λ x8 : ι → ι . λ x9 . x1 (λ x10 x11 . λ x12 : ι → ι . λ x13 . x12 0) (λ x10 : ι → ι → ι → ι . λ x11 x12 . x2 (λ x13 x14 x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) 0) (λ x8 . 0) (setsum (x7 (λ x8 : ι → ι . 0) (λ x8 : ι → ι . λ x9 . 0) (λ x8 . 0) 0) (setsum 0 0)))) 0.
Assume H1:
∀ x4 : (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . λ x9 : ((ι → ι) → ι) → ι . λ x10 . setsum (x2 (λ x11 x12 x13 : ι → ι . λ x14 . x12 0) (λ x11 : (ι → ι → ι) → ι . x9 (λ x12 : ι → ι . x2 (λ x13 x14 x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0)) 0 x7) (setsum x8 (Inj1 0))) (λ x8 : (ι → ι) → ι → ι . setsum (Inj0 0) 0) 0 = Inj1 (x1 (λ x8 x9 . λ x10 : ι → ι . λ x11 . x0 (λ x12 x13 x14 . x2 (λ x15 x16 x17 : ι → ι . λ x18 . 0) (λ x15 : (ι → ι → ι) → ι . x14) x11 0) (Inj1 0)) (λ x8 : ι → ι → ι → ι . λ x9 x10 . x0 (λ x11 x12 x13 . setsum (x1 (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x14 : ι → ι → ι → ι . λ x15 x16 . 0) 0) x11) (x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . setsum 0 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . Inj1 0) x9)) (Inj0 (setsum (x2 (λ x8 x9 x10 : ι → ι . λ x11 . 0) (λ x8 : (ι → ι → ι) → ι . 0) 0 0) (setsum 0 0)))).
Assume H2:
∀ 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 . x2 (λ x8 x9 x10 : ι → ι . λ x11 . 0) (λ x8 : (ι → ι → ι) → ι . x7 (setsum (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x8 (λ x12 x13 . 0)) (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0) 0) (x6 (x7 0) (λ x9 . x6 0 (λ x10 . 0))))) (x7 (Inj1 (Inj0 (setsum 0 0)))) (setsum 0 (x5 (λ x8 x9 : ι → ι . Inj1 (x1 (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : ι → ι → ι → ι . λ x11 x12 . 0) 0)) ...)) = ....