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