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