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