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