Let x0 of type ((ι → CT2 ι) → CT3 ι) → (ι → ι → ι → ι → ι) → CT2 ι be given.
Let x1 of type (ι → ι → ι) → ((CT2 ι) → ι) → ι → (ι → ι) → ι → ι → ι be given.
Let x2 of type ((ι → ((ι → ι) → ι) → ι → ι) → (CT2 ι) → 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 → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x8 : ι → ι . 0) 0 x6 (x1 (λ x8 x9 . setsum 0 (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x10 : ι → ι . x8) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0)) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0)) (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0) 0 0))) (λ x8 : (ι → ι → ι) → ι . x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . Inj1 (Inj0 0)) (λ x9 : ι → ι . x1 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0) (x9 0) (λ x10 . 0) (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0) (x9 0)) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0) (λ x9 x10 x11 x12 . x9) (λ x9 x10 . Inj1 0)) (x7 0) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0)))) (x1 (λ x8 x9 . 0) (λ x8 : (ι → ι → ι) → ι . x5 (λ x9 : ι → ι → ι . 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0))) (x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . x6) (λ x8 x9 x10 x11 . setsum 0 0) (λ x8 x9 . Inj0 0)) (λ x8 . 0) (Inj0 (x3 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x8 : ι → ι . 0) 0 0 0)) (x1 (λ x8 x9 . 0) (λ x8 : (ι → ι → ι) → ι . x7 0) (x2 (λ x8 : ι → ((ι → ι) → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 : ι → ι . 0)) (λ x8 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0)) (x3 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x8 : ι → ι . 0) 0 0 0) (x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 x9 x10 x11 . 0) (λ x8 x9 . 0)))) (λ x8 . Inj1 0) (x2 (λ x8 : ι → ((ι → ι) → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 : ι → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x8 0) (λ x9 x10 x11 x12 . x2 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0)) (λ x9 x10 . Inj0 0))) (x5 (λ x8 : ι → ι → ι . setsum (x8 0 0) (x5 (λ x9 : ι → ι → ι . 0) 0)) 0)) = x6.
Assume H1:
∀ x4 x5 x6 x7 . x3 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 (x1 (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . x2 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0)) (λ x11 x12 x13 x14 . x0 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 x16 x17 x18 . 0) (λ x15 x16 . 0)) ...) ... ... ... ... ...)) ... 0 ... ... = ....