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