Let x0 of type (((ι → ι → ι) → ι → ι) → (((ι → ι) → ι) → ι) → CT2 ι) → ι → ι be given.
Let x1 of type (ι → ι → ι → (ι → ι) → ι) → (ι → ι) → ((ι → ι) → (ι → ι) → ι → ι) → ι be given.
Let x2 of type (CT2 ι) → (ι → ((ι → ι) → ι) → ι) → ι → ι be given.
Let x3 of type (ι → ι) → ι → ι be given.
Assume H0:
∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . Inj1 (x3 (λ x9 . x3 (λ x10 . Inj0 0) (x3 (λ x10 . 0) 0)) 0)) x5 = x5.
Assume H1:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 . x2 (λ x9 : ι → ι → ι . x9 (Inj0 0) (x1 (λ x10 x11 x12 . λ x13 : ι → ι . x0 (λ x14 : (ι → ι → ι) → ι → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι → ι . 0) 0) (λ x10 . x2 (λ x11 : ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0) (λ x10 x11 : ι → ι . λ x12 . x10 0))) (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 : (ι → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . x11 (λ x14 x15 . 0) (x0 (λ x14 : (ι → ι → ι) → ι → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι → ι . 0) 0)) (Inj0 0)) 0) (x0 (λ x8 : (ι → ι → ι) → ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . x7) x6) = x0 (λ x8 : (ι → ι → ι) → ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . Inj0 (Inj0 (x2 (λ x11 : ι → ι → ι . x11 0 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) x7))) (x0 (λ x8 : (ι → ι → ι) → ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . 0) x6).
Assume H2:
∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι → ι → ι . x2 (λ x8 : ι → ι → ι . x8 (setsum 0 (x3 (λ x9 . 0) (x8 0 0))) (setsum (x0 (λ x9 : (ι → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . 0) 0) (x1 (λ x9 x10 x11 . λ x12 : ι → ι . x9) (λ x9 . setsum 0 0) (λ x9 x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → ι → ι) → ι → ι . λ x13 : ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . 0) 0)))) (λ x8 . λ x9 : (ι → ι) → ι . x1 (λ x10 x11 x12 . λ x13 : ι → ι . 0) (λ x10 . x0 (λ x11 : (ι → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . x11 (λ x14 x15 . 0) 0) (x0 (λ x11 : (ι → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . 0) (x2 (λ x11 : ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0))) (λ x10 x11 : ι → ι . λ x12 . setsum 0 (x1 (λ x13 x14 x15 . λ x16 : ι → ι . setsum 0 0) (λ x13 . x3 (λ x14 . 0) 0) (λ x13 x14 : ι → ι . λ x15 . x3 (λ x16 . 0) 0)))) (x6 (Inj1 (x6 (x3 (λ x8 . 0) 0)))) = Inj0 (setsum (Inj1 (x6 0)) 0).
Assume H3:
∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x8 : ι → ι → ι . 0) (λ x8 . λ x9 : (ι → ι) → ι . Inj1 (Inj1 (Inj1 (setsum 0 0)))) x6 = Inj1 (Inj0 (x1 (λ x8 x9 x10 . λ x11 : ι → ι . x8) (λ x8 . 0) (λ x8 x9 : ι → ι . λ x10 . 0))).
Assume H4:
∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 x9 x10 . λ x11 : ι → ι . setsum (x1 (λ x12 x13 x14 . λ x15 : ι → ι . x12) (λ x12 . Inj0 x12) (λ x12 x13 : ι → ι . λ x14 . 0)) (x1 (λ x12 x13 x14 . λ x15 : ι → ι . setsum (x1 (λ x16 x17 x18 . λ x19 : ι → ι . 0) (λ x16 . 0) ...) ...) ... ...)) ... ... = ....