Let x0 of type (CT4 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) → ι) → (ι → ι) → (((ι → ι) → ι) → (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) → (ι → ι) → ι be given.
Assume H0:
∀ x4 . ∀ x5 : (ι → ι → ι) → (ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι . x1 (λ x9 : (ι → ι) → ι . x2 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 . x9 (λ x11 . x2 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0))) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . setsum (x0 (λ x13 : ι → ι → ι → ι → ι . 0) (λ x13 . 0)) 0)) (setsum (x0 (λ x9 : ι → ι → ι → ι → ι . x6) (λ x9 . x8 (λ x10 : (ι → ι) → ι → ι . 0) 0)) (x1 (λ x9 : (ι → ι) → ι . Inj0 0) (setsum 0 0) (λ x9 : ι → ι → ι . λ x10 x11 . 0) (x2 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0)) (λ x9 . setsum 0 0))) (λ x9 : ι → ι → ι . λ x10 x11 . x11) (x0 (λ x9 : ι → ι → ι → ι → ι . x6) (λ x9 . x6)) (λ x9 . x1 (λ x10 : (ι → ι) → ι . x9) (setsum (x8 (λ x10 : (ι → ι) → ι → ι . 0) 0) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 . 0) (λ x10 . 0))) (λ x10 : ι → ι → ι . λ x11 x12 . setsum (setsum 0 0) (x0 (λ x13 : ι → ι → ι → ι → ι . 0) (λ x13 . 0))) (x2 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 : (ι → ι) → ι . Inj0 0) (λ x10 . x8 (λ x11 : (ι → ι) → ι → ι . 0) 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . setsum 0 0)) (λ x10 . 0))) x6 (λ x8 : ι → ι → ι . λ x9 . x7) (λ x8 . 0) = x6.
Assume H1:
∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . x3 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι . x1 (λ x9 : (ι → ι) → ι . x7 (x9 (λ x10 . Inj0 0)) (λ x10 : ι → ι . 0) (λ x10 . x8 (λ x11 : (ι → ι) → ι → ι . x10) (x9 (λ x11 . 0))) 0) 0 (λ x9 : ι → ι → ι . λ x10 x11 . 0) (x2 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x8 (λ x12 : (ι → ι) → ι → ι . x9 (λ x13 . 0)) 0)) (λ x9 . x0 (λ x10 : ι → ι → ι → ι → ι . 0) (λ x10 . x8 (λ x11 : (ι → ι) → ι → ι . 0) (Inj1 0)))) (x2 (λ x8 . λ x9 : ι → ι → ι → ι . λ x10 : (ι → ι) → ι . 0) (λ x8 . 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . x7 (x2 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 : (ι → ι) → ι . x1 (λ x14 : (ι → ι) → ι . 0) 0 (λ x14 : ι → ι → ι . λ x15 x16 . 0) 0 (λ x14 . 0)) (λ x11 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . setsum 0 0)) (λ x11 : ι → ι . x9 0) (λ x11 . Inj1 0) (x1 (λ x11 : (ι → ι) → ι . x0 (λ x12 : ι → ι → ι → ι → ι . 0) (λ x12 . 0)) (x8 (λ x11 . 0)) (λ x11 : ι → ι → ι . λ x12 x13 . Inj1 0) (Inj1 0) (λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . 0) 0 (λ x12 : ι → ι → ι . λ x13 . 0) (λ x12 . 0))))) ... ... = ....