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 be given.
Let x2 of type (((ι → ι) → CT2 ι) → (ι → (ι → ι) → 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 be given.
Assume H0:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x8 : ι → (ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . setsum 0 x9) 0) 0 (λ x8 x9 x10 . 0) (x1 (λ x8 . λ x9 : ι → ι . x6) (setsum (x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . setsum 0 0) 0 (x5 0)) (setsum (x2 (λ x8 : (ι → ι) → (ι → ι → ι) → ι . λ x9 : ι → (ι → ι) → ι . λ x10 . 0) (λ x8 . 0)) (x5 0)))) = setsum 0 x6.
Assume H1:
∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x8 : ι → (ι → ι → ι) → ι → ι . setsum (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . x3 (λ x15 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x15 x16 x17 . 0) 0) (λ x12 . x11 (λ x13 . 0))) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x7 0 (λ x10 x11 . 0)) (Inj0 0) (λ x9 x10 x11 . 0) 0) 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (setsum (x6 0) (Inj1 0)) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x10 0 (λ x12 . 0)) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) 0)))) (x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 : ι → (ι → ι → ι) → ι → ι . x9) (setsum (x7 0 (λ x11 x12 . 0)) (x3 (λ x11 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x11 x12 x13 . 0) 0)) (λ x11 x12 x13 . 0) x8) (x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . 0) x4 (x7 (x2 (λ x8 : (ι → ι) → (ι → ι → ι) → ι . λ x9 : ι → (ι → ι) → ι . λ x10 . 0) (λ x8 . 0)) (λ x8 x9 . x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . 0) (λ x10 . 0)))) (setsum (setsum (setsum 0 0) 0) (x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . x8) (setsum 0 0) (x3 (λ x8 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x8 x9 x10 . 0) 0)))) (λ x8 x9 x10 . 0) 0 = x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . setsum 0 (x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . x3 (λ x14 : ι → (ι → ι → ι) → ι → ι . x1 (λ x15 . λ x16 : ι → ι . 0) 0) 0 (λ x14 x15 x16 . x3 (λ x17 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x17 x18 x19 . 0) 0) 0) (λ x11 . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x9) (Inj0 0) (λ x12 x13 x14 . setsum 0 0) 0))) (x2 (λ x8 : (ι → ι) → (ι → ι → ι) → ι . λ x9 : ι → (ι → ι) → ι . λ x10 . 0) (λ x8 . setsum 0 0)) (x6 (x1 (λ x8 . λ x9 : ι → ι . 0) (Inj1 (x1 (λ x8 . λ x9 : ι → ι . 0) 0)))).
Assume H2:
∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x8 : (ι → ι) → (ι → ι → ι) → ι . λ x9 : ι → (ι → ι) → ι . λ x10 . x10) (λ x8 . 0) = x4 (λ x8 : (ι → ι) → ι → ι . λ x9 . Inj0 (x8 (λ x10 . setsum (x1 (λ x11 . λ x12 : ι → ι . 0) 0) (x2 ... ...)) ...)) 0.