Let x0 of type (((ι → ι) → ι → (ι → ι) → ι → ι) → ι) → ι → ι be given.
Let x1 of type (ι → ι) → ι → ι be given.
Let x2 of type ((ι → ι) → ι) → ((CT2 ι) → ι) → ι be given.
Let x3 of type (ι → ι) → ((CN (ι → ι)) → ((ι → ι) → ι) → ι → ι) → ι be given.
Assume H0:
∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x3 (λ x8 . Inj1 (x3 (λ x9 . x3 (λ x10 . x7 (λ x11 : (ι → ι) → ι → ι . 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . Inj1 0)) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 . x2 (λ x11 : ι → ι . x2 (λ x12 : ι → ι . x9 (λ x13 . Inj0 0)) (λ x12 : (ι → ι → ι) → ι . x10)) (λ x11 : (ι → ι → ι) → ι . 0)) = x2 (λ x8 : ι → ι . x3 (λ x9 . Inj0 (x2 (λ x10 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x0 (λ x12 : (ι → ι) → ι → (ι → ι) → ι → ι . Inj0 (Inj0 0)) (x2 (λ x12 : ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . Inj0 0)))) (λ x8 : (ι → ι → ι) → ι . x7 (λ x9 : (ι → ι) → ι → ι . Inj0 (setsum (Inj0 0) (x2 (λ x10 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0))))).
Assume H1:
∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . setsum x8 0) x8) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 . x1 (λ x11 . 0) (setsum (Inj0 x10) 0)) = setsum (x3 (λ x8 . Inj0 (x3 (λ x9 . x1 (λ x10 . 0) 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x10 (λ x12 . 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 . x0 (λ x11 : (ι → ι) → ι → (ι → ι) → ι → ι . x9 (λ x12 . Inj0 0)) x10)) (Inj1 (x4 (Inj1 x7))).
Assume H2:
∀ x4 : (ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 : ι → ι . x5) (λ x8 : (ι → ι → ι) → ι . 0) = setsum (x3 (λ x8 . 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 . x1 (λ x11 . x9 (λ x12 . x10)) (Inj1 x10))) (setsum (x6 0) (x3 (λ x8 . x5) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 . 0))).
Assume H3:
∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 . x2 (λ x8 : ι → ι . Inj1 0) (λ x8 : (ι → ι → ι) → ι . Inj0 (setsum (x3 (λ x9 . x3 (λ x10 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . 0)) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0))) (x6 (λ x9 . 0) (λ x9 : ι → ι . x9 0)))) = Inj1 0.
Assume H4:
∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . x1 (λ x8 . x8) 0 = setsum 0 0.
Assume H5:
∀ x4 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x1 (λ x8 . 0) (x6 (λ x8 . Inj1 (x1 (λ x9 . x6 (λ x10 . 0) 0 (λ x10 . 0)) 0)) (setsum x7 (x2 (λ x8 : ι → ι . 0) (λ x8 : (ι → ι → ι) → ι . 0))) (λ x8 . 0)) = Inj1 x7.
Assume H6: ∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : (ι → ι) → ι → (ι → ι) → ι → ι . ...) ... = ....