Let x0 of type (ι → ι → ι) → ((CT2 ι) → ((ι → ι) → 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 be given.
Let x2 of type (ι → CT2 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 be given.
Assume H0:
∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) x7 (x8 (λ x11 x12 . x2 (λ x13 . λ x14 : ι → ι → ι . 0) (λ x13 : ι → ι . x11)) (x10 (λ x11 . x1 (λ x12 . 0) 0 0 0 0 0) (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0 0)) (setsum 0 (Inj0 0)) x7)) (x5 0 (λ x8 : ι → ι . 0)) (x1 (λ x8 . x7) (x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . 0) 0 (x1 (λ x8 . setsum 0 0) 0 0 (x2 (λ x8 . λ x9 : ι → ι → ι . 0) (λ x8 : ι → ι . 0)) (Inj0 0) 0)) (Inj0 0) (x0 (λ x8 x9 . 0) (λ x8 : (ι → ι → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 . 0) (λ x8 : (ι → ι) → ι . x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . 0)) 0 (x0 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . 0) (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . 0))) (λ x8 : ι → ι . λ x9 . setsum 0 (x6 0))) (x5 (x2 (λ x8 . λ x9 : ι → ι → ι . x2 (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 : ι → ι . 0)) (λ x8 : ι → ι . x8 0)) (λ x8 : ι → ι . x5 (Inj0 0) (λ x9 : ι → ι . x8 0))) (Inj1 (Inj1 (x2 (λ x8 . λ x9 : ι → ι → ι . 0) (λ x8 : ι → ι . 0))))) = Inj1 (Inj1 0).
Assume H1:
∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 : (ι → ι → ι) → ι → ι → ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . x0 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . x1 (λ x14 . x14) 0 (setsum (x10 (λ x14 . 0) 0) (x3 (λ x14 : (ι → ι → ι) → ι → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) 0 0)) 0 0 (Inj1 (x12 (λ x14 . 0) 0))) (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . λ x12 . 0)) (Inj1 (setsum (x4 (x6 0) (λ x8 . x6 0)) 0)) 0 = x0 (λ x8 x9 . x2 (λ x10 . λ x11 : ι → ι → ι . x11 (x1 (λ x12 . Inj0 0) 0 x8 (setsum 0 0) (x3 (λ x12 : (ι → ι → ι) → ι → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0 0) 0) (Inj0 0)) (λ x10 : ι → ι . Inj1 (setsum (x2 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 : ι → ι . 0)) 0))) (λ x8 : (ι → ι → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 . 0) (setsum (Inj0 (x2 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 : ι → ι . 0))) 0) 0 0 0 ...) ... ....