Let x0 of type (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) → ι) → ι be given.
Let x2 of type ((ι → ((ι → ι) → 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 → ι) → ι) → CT2 ι) → ι → ι be given.
Assume H0:
∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x3 (λ x8 : ((ι → ι → ι) → ι → ι) → ι . λ x9 : ι → ι → ι . x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum (Inj1 (Inj0 0)) (x9 (Inj1 0) (Inj0 0))) (x0 (λ x10 . x10) (λ x10 x11 . λ x12 : ι → ι . setsum (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0)) (setsum 0 0)))) (x2 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . 0) x5) (x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x7 (λ x10 . 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum 0 0) (x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . 0)))) (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x8) x4) = setsum x5 x4.
Assume H1:
∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x8 : ((ι → ι → ι) → ι → ι) → ι . λ x9 : ι → ι → ι . 0) 0 = setsum 0 (x4 (λ x8 . λ x9 : ι → ι . 0)).
Assume H2:
∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . Inj0 (Inj0 (setsum 0 0)))) (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum (x0 (λ x11 . setsum x11 (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . 0))) (λ x11 x12 . λ x13 : ι → ι . setsum (setsum 0 0) (Inj1 0))) (setsum 0 (setsum (setsum 0 0) (x3 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . 0) 0)))) (x4 (x3 (λ x8 : ((ι → ι → ι) → ι → ι) → ι . λ x9 : ι → ι → ι . 0) (setsum (Inj0 0) 0)) (λ x8 . setsum 0 (Inj0 0)) (λ x8 . setsum 0 (setsum 0 (x5 0 0 (λ x9 . 0)))) (x1 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x8 : ι → (ι → ι) → ι . 0))) = x0 (λ x8 . x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . setsum (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . 0)) (Inj1 x10))) (λ x8 x9 . λ x10 : ι → ι . setsum (x7 (setsum x9 (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 : ι → (ι → ι) → ι . 0)))) 0).
Assume H3:
∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum 0 (setsum (setsum (x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) 0) (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . 0) 0)) 0)) (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum (setsum 0 x7) (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 : ((ι → ι → ι) → ι → ι) → ι . λ x17 : ι → ι → ι . x14 0) x12) (λ x11 : ι → (ι → ι) → ι . Inj1 (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) ...)))) 0 = ....