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