Let x0 of type ((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 → ι) → ι) → ι → ι → ι) → ι → CT3 ι be given.
Let x3 of type (ι → ι → ((ι → ι) → ι) → ι) → ι → (CT2 ι) → ι → (ι → ι) → ι be given.
Assume H0:
∀ x4 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . 0) (Inj1 x9) (λ x11 : ι → ι → ι . Inj1 (setsum (x0 (λ x12 : ι → ι . 0) 0) (Inj1 0))) (Inj1 (x1 (λ x11 . 0) (x1 (λ x11 . 0) 0))) (λ x11 . x1 (λ x12 . setsum (Inj1 0) x12) (setsum (x1 (λ x12 . 0) 0) (setsum 0 0)))) (setsum (setsum 0 (setsum (x1 (λ x8 . 0) 0) (x1 (λ x8 . 0) 0))) (x1 (λ x8 . 0) (x2 (λ x8 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . x2 (λ x11 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x12 x13 . 0) 0 (λ x11 x12 x13 . 0)) (x1 (λ x8 . 0) 0) (λ x8 x9 x10 . Inj1 0)))) (λ x8 : ι → ι → ι . setsum (x0 (λ x9 : ι → ι . 0) (x1 (λ x9 . Inj1 0) (x1 (λ x9 . 0) 0))) 0) x7 (λ x8 . x1 (λ x9 . 0) (x2 (λ x9 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . 0) (Inj1 (x2 (λ x9 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . 0) 0 (λ x9 x10 x11 . 0))) (λ x9 x10 x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . x11) x10 (λ x12 : ι → ι → ι . setsum 0 0) 0 (λ x12 . x10)))) = x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . Inj0 (setsum (x1 (λ x11 . 0) (Inj0 0)) (setsum (x10 (λ x11 . 0)) x8))) (x0 (λ x8 : ι → ι . x2 (λ x9 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . 0) 0 (λ x9 x10 x11 . 0)) 0) (λ x8 : ι → ι → ι . Inj0 (x2 (λ x9 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . 0) (x2 (λ x9 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . x1 (λ x12 . 0) 0) 0 (λ x9 x10 x11 . 0)) (λ x9 x10 x11 . x11))) (x4 (λ x8 : (ι → ι) → ι . x8 (λ x9 . x0 (λ x10 : ι → ι . Inj1 0) (x8 (λ x10 . 0)))) (λ x8 : ι → ι . λ x9 . Inj0 (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0))) (x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . x10 (λ x11 . 0)) (x6 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . 0)) (λ x8 : ι → ι → ι . x0 (λ x9 : ι → ι . Inj0 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : ι → ι → ι . 0) 0 (λ x9 . 0))) 0 (λ x8 . x1 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) 0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 . 0)) 0))) (λ x8 . Inj1 (x2 (λ x9 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . Inj0 (x1 (λ x12 . 0) 0)) (Inj0 0) (λ x9 x10 x11 . x8))).
Assume H1: ∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . 0) (x5 (x2 (λ x8 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . ...) ... ...)) ... ... ... = ....