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