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