Let x0 of type ((ι → (ι → ι) → ι → ι → ι) → ι) → (ι → ι) → ι → ι be given.
Let x1 of type (ι → ι → ι) → ι → ι be given.
Let x2 of type (CT3 ι) → ι → ι → ι be given.
Let x3 of type (ι → (CN (ι → ι)) → ι) → ((CT2 ι) → ι) → ι → ((ι → ι) → ι → ι) → ι → ι → ι be given.
Assume H0:
∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x8) (λ x8 : (ι → ι → ι) → ι . x5 (λ x9 : ι → ι → ι . x6) (setsum (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . Inj0 0) (λ x9 . x9) (setsum 0 0)) (setsum (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . 0) (λ x9 . 0) 0) (Inj1 0)))) (x2 (λ x8 : ι → ι → ι → ι . 0) (setsum (x1 (λ x8 x9 . x1 (λ x10 x11 . 0) 0) (Inj1 0)) (x0 (λ x8 : ι → (ι → ι) → ι → ι → ι . setsum 0 0) (λ x8 . x8) (x0 (λ x8 : ι → (ι → ι) → ι → ι → ι . 0) (λ x8 . 0) 0))) 0) (λ x8 : ι → ι . λ x9 . x1 (λ x10 x11 . x9) 0) (x1 (λ x8 x9 . 0) (x2 (λ x8 : ι → ι → ι → ι . x5 (λ x9 : ι → ι → ι . Inj1 0) (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)) (Inj1 (Inj0 0)) 0)) (x0 (λ x8 : ι → (ι → ι) → ι → ι → ι . x6) (λ x8 . Inj1 (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x11 : ι → (ι → ι) → ι → ι → ι . 0) (λ x11 . 0) 0) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) x7 (λ x9 : ι → ι . λ x10 . 0) (x1 (λ x9 x10 . 0) 0) x8)) (setsum (setsum 0 x4) 0)) = x0 (λ x8 : ι → (ι → ι) → ι → ι → ι . x6) (λ x8 . x2 (λ x9 : ι → ι → ι → ι . Inj1 (x1 (λ x10 x11 . 0) (setsum 0 0))) 0 (x1 (λ x9 x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x13 : ι → (ι → ι) → ι → ι → ι . 0) (λ x13 . 0) 0) (λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . 0)) x8 (λ x11 : ι → ι . λ x12 . x12) 0 (Inj1 0)) (x2 (λ x9 : ι → ι → ι → ι . x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . 0) (λ x10 . 0) 0) (setsum 0 0) (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . 0) (λ x9 . 0) 0)))) (Inj0 (x3 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x10 : ι → ι → ι → ι . x0 (λ x11 : ι → (ι → ι) → ι → ι → ι . 0) (λ x11 . 0) 0) (x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . 0) (λ x10 . 0) 0) 0) (λ x8 : (ι → ι → ι) → ι . Inj1 0) (x1 (λ x8 x9 . x2 (λ x10 : ι → ι → ι → ι . 0) 0 0) 0) (λ x8 : ι → ι . λ x9 . x8 (Inj0 0)) (Inj1 x4) (Inj1 0))).
Assume H1:
∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x7) (λ x8 : (ι → ι → ι) → ι . x1 (λ x9 x10 . x2 (λ x11 : ι → ι → ι → ι . setsum x9 x10) (Inj0 (Inj0 0)) (x2 (λ x11 : ι → ι → ι → ι . x2 (λ x12 : ι → ι → ι → ι . 0) 0 0) 0 (x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) ... 0 ... 0 0))) ...) ... ... ... ... = ....