Let x0 of type (ι → ι → ι) → ((CT2 ι) → ι → ι) → ι be given.
Let x1 of type ((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 → 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 be given.
Assume H0:
∀ x4 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x8 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x1 (λ x9 : ι → ι . λ x10 : ι → (ι → ι) → ι . Inj1 0) (x1 (λ x9 : ι → ι . λ x10 : ι → (ι → ι) → ι . x1 (λ x11 : ι → ι . λ x12 : ι → (ι → ι) → ι . x3 (λ x13 : ((ι → ι) → (ι → ι) → ι → ι) → ι . 0) 0 0) (Inj0 0)) (x2 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 x13 . setsum 0 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 . 0)))) (x3 (λ x8 : ((ι → ι) → (ι → ι) → ι → ι) → ι . Inj0 (x0 (λ x9 x10 . x10) (λ x9 : (ι → ι → ι) → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 : ι → (ι → ι) → ι . 0) 0))) x6 (x2 (λ x8 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x9 x10 x11 x12 . x9) (λ x8 : ((ι → ι) → ι → ι) → ι . λ x9 . x2 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 x14 . setsum 0 0) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . setsum 0 0)))) (x2 (λ x8 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x9 x10 x11 x12 . setsum 0 x12) (λ x8 : ((ι → ι) → ι → ι) → ι . λ x9 . x3 (λ x10 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x12 x13 x14 x15 . x2 (λ x16 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x17 x18 x19 x20 . 0) (λ x16 : ((ι → ι) → ι → ι) → ι . λ x17 . 0)) (λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . Inj1 0)) (x0 (λ x10 x11 . Inj0 0) (λ x10 : (ι → ι → ι) → ι . λ x11 . 0)) (setsum x9 0))) = x1 (λ x8 : ι → ι . λ x9 : ι → (ι → ι) → ι . x7 (λ x10 . λ x11 : ι → ι . λ x12 . x9 (Inj0 (Inj0 0)) (λ x13 . Inj0 0)) (λ x10 : ι → ι . λ x11 . 0)) (setsum 0 (Inj1 (x3 (λ x8 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x3 (λ x9 : ((ι → ι) → (ι → ι) → ι → ι) → ι . 0) 0 0) x6 (x1 (λ x8 : ι → ι . λ x9 : ι → (ι → ι) → ι . 0) 0)))).
Assume H1:
∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x8 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x9 x10 . setsum 0 (x2 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x12 x13 x14 x15 . setsum 0 0) (λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . 0))) (λ x9 : (ι → ι → ι) → ι . λ x10 . Inj1 0)) (x0 (λ x8 x9 . x9) (λ x8 : (ι → ι → ι) → ι . λ x9 . Inj0 (x8 (λ x10 x11 . setsum 0 0)))) (Inj0 (Inj0 (x0 (λ x8 x9 . Inj0 0) (λ x8 : (ι → ι → ι) → ι . λ x9 . Inj1 0)))) = Inj1 (x3 (λ x8 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0)) (Inj0 (Inj0 0)) (x5 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . x7 (x3 (λ x10 : ((ι → ι) → (ι → ι) → ι → ι) → ι . 0) 0 0) (λ x10 : ι → ι . Inj0 0)))).
Assume H2:
∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x9 x10 x11 x12 . x10) (λ x8 : ((ι → ι) → ι → ι) → ι . λ x9 . Inj1 (setsum (x7 (x3 (λ x10 : ((ι → ι) → (ι → ι) → ι → ι) → ι . 0) 0 0)) 0)) = Inj1 (x0 (λ x8 x9 . x6 0) (λ x8 : (ι → ι → ι) → ι . λ x9 . x7 (x8 (λ x10 x11 . Inj0 0)))).
Assume H3:
∀ x4 x5 . ∀ x6 x7 : (ι → ι) → ι . x2 (λ x8 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x9 x10 x11 x12 . 0) (λ x8 : ((ι → ι) → ι → ι) → ι . λ x9 . x7 (λ x10 . setsum (x8 (λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 . 0))) 0)) = ....