Let x0 of type (ι → ι) → (ι → ι) → (CN (ι → ι)) → ι → ι → ι be given.
Let x1 of type (ι → ι) → ι → (CT2 ι) → (ι → ι) → ι be given.
Let x2 of type (((ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (CT2 ι) → ((ι → ι) → ι → ι) → ι) → ι → CT2 ι be given.
Let x3 of type (ι → ι → ((ι → ι) → ι) → (ι → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x0 (λ x12 . setsum (setsum 0 x12) 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) (x10 (λ x12 . x11 (x11 0))) (Inj1 (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0)))) 0 = x0 (λ x8 . setsum x8 (x0 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x2 (λ x14 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . λ x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 x15 . 0)) x8) (λ x9 . x9) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . Inj0 (setsum 0 0)) x6 x8)) (λ x8 . setsum (x0 (λ x9 . 0) (λ x9 . x9) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x8) (Inj0 0) (setsum (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0))) x8) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . Inj1 0) 0) (Inj0 0) (λ x11 x12 . Inj0 (Inj1 0))) (x9 (x9 0))) (x0 (λ x8 . x8) (λ x8 . x2 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) 0) (setsum (x1 (λ x9 . 0) 0 (λ x9 : ι → ι → ι . 0) (λ x9 . 0)) (x0 (λ x9 . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 0)) (λ x9 x10 . x8)) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . x2 (λ x11 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . x11 (λ x14 x15 x16 . x2 (λ x17 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x18 : (ι → ι → ι) → ι . λ x19 : (ι → ι) → ι → ι . 0) 0 (λ x17 x18 . 0)) (λ x14 : ι → ι . Inj1 0) (λ x14 . Inj1 0) (setsum 0 0)) (x0 (λ x11 . setsum 0 0) (λ x11 . x11) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . setsum 0 0) (x9 0) 0) (λ x11 x12 . x12)) (x7 (x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum 0 0) 0)) x6) (x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . x2 (λ x15 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → ι . λ x17 : (ι → ι) → ι → ι . 0) (x0 (λ x15 . 0) (λ x15 . 0) (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0) 0 0) (λ x15 x16 . x1 (λ x17 . 0) 0 (λ x17 : ι → ι → ι . 0) (λ x17 . 0))) (x11 (x1 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . 0) (λ x12 . 0))) (λ x12 x13 . x1 (λ x14 . x12) ... ... ...)) 0).