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