Let x0 of type (ι → (ι → (ι → ι) → 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) → ι → ι be given.
Let x2 of type ((((ι → ι) → (ι → ι) → ι) → ι → ι) → (ι → ι) → ι) → CT2 ι be given.
Let x3 of type ((ι → ι) → (((ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι → ι be given.
Assume H0:
∀ x4 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 . 0) (x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 x11) 0) = Inj1 (x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . λ x12 x13 . x10 (x0 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . λ x16 : ι → ι → ι . λ x17 x18 . 0) 0) (λ x14 . x14) 0) (setsum (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 x10 . 0)) 0)) x7).
Assume H1:
∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι → ι) → ι . x1 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . Inj1 x10) (λ x10 : (ι → ι) → ι → ι . Inj0 (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . x12 0 (λ x16 . 0) 0) (x10 (λ x11 . 0) 0))) (x1 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . setsum (x1 (λ x12 . λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . 0) 0) (x2 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 x13 . 0))) (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x10 (λ x13 . 0) 0) (λ x11 . x2 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 x13 . 0)) (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0)) (setsum (Inj1 0) (x7 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0))))) (λ x8 . Inj0 (Inj1 (Inj1 (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 x10 . 0))))) (x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x9 : ι → ι . x9 (x6 0)) (λ x8 x9 . x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 : ι → ι → ι . λ x15 x16 . x13 0 (λ x17 . 0) 0) (setsum 0 0)) (λ x10 . x9) (x1 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0) (setsum 0 0)))) = setsum (x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 : ι → ι → ι . λ x11 x12 . x9 (setsum 0 0) (λ x13 . x12) (Inj0 (x9 0 (λ x13 . 0) 0))) (x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x9 : ι → ι . 0) (λ x8 x9 . x6 (x1 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . 0) 0)))) 0.
Assume H2:
∀ x4 x5 x6 x7 . x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x9 : ι → ι . 0) (λ x8 x9 . x1 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . 0) (setsum (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . λ x13 x14 . setsum 0 0) x8) (x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι . x2 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 x13 . 0)) (λ x10 . 0) 0))) = setsum x7 (Inj0 0).
Assume H3: ∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 ... ... = ....