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