Let x0 of type (ι → (CT2 ι) → ι) → (ι → ι) → (ι → ι) → ι → ι → ι → ι be given.
Let x1 of type ((ι → (ι → ι) → (ι → ι) → ι → ι) → ι) → CT4 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 ((CT2 ι) → ι → ι → (ι → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι . x3 (λ x8 : (ι → ι → ι) → ι . λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 x13 : (ι → ι) → ι . setsum (setsum 0 0) x10) (λ x12 . λ x13 : ι → ι . x1 (λ x14 : ι → (ι → ι) → (ι → ι) → ι → ι . Inj1 (x0 (λ x15 . λ x16 : (ι → ι → ι) → ι . 0) (λ x15 . 0) (λ x15 . 0) 0 0 0)) (λ x14 x15 x16 x17 . x17)) (x1 (λ x12 : ι → (ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 x13 x14 x15 . x15)) (x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . x13 (λ x14 x15 . x14)) (λ x12 . x10) (λ x12 . x3 (λ x13 : (ι → ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . 0) (x3 (λ x13 : (ι → ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0)) (setsum 0 (x11 0)) (x8 (λ x12 x13 . x2 (λ x14 x15 : (ι → ι) → ι . 0) (λ x14 . λ x15 : ι → ι . 0) 0 0)) (x3 (λ x12 : (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . x13) (Inj1 0)))) (setsum (x2 (λ x8 x9 : (ι → ι) → ι . x8 (λ x10 . setsum 0 0)) (λ x8 . λ x9 : ι → ι . x0 (λ x10 . λ x11 : (ι → ι → ι) → ι . x3 (λ x12 : (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0) (λ x10 . x8) (λ x10 . x2 (λ x11 x12 : (ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . 0) 0 0) (x9 0) (setsum 0 0) 0) x6 (setsum (Inj0 0) 0)) x4) = x2 (λ x8 x9 : (ι → ι) → ι . x0 (λ x10 . λ x11 : (ι → ι → ι) → ι . setsum (setsum (x11 (λ x12 x13 . 0)) (x11 (λ x12 x13 . 0))) 0) (λ x10 . 0) (λ x10 . Inj0 (x7 (λ x11 . x10) (x8 (λ x11 . 0)) (λ x11 . Inj0 0))) 0 0 0) (λ x8 . λ x9 : ι → ι . x7 (λ x10 . x1 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . Inj0 (x2 (λ x12 x13 : (ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . 0) 0 0)) (λ x11 x12 x13 x14 . setsum (x0 (λ x15 . λ x16 : (ι → ι → ι) → ι . 0) (λ x15 . 0) (λ x15 . 0) 0 0 0) (setsum 0 0))) (Inj1 x6) (λ x10 . x9 (x9 (x9 0)))) (x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . setsum (x2 (λ x10 x11 : (ι → ι) → ι . x10 (λ x12 . 0)) (λ x10 . λ x11 : ι → ι . Inj0 0) (x9 (λ x10 x11 . 0)) (Inj1 0)) (x0 (λ x10 . λ x11 : (ι → ι → ι) → ι . Inj0 0) (λ x10 . 0) (λ x10 . x7 (λ x11 . 0) 0 (λ x11 . 0)) x8 0 (Inj0 0))) (λ x8 . x3 (λ x9 : (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . 0) (x2 (λ x9 x10 : (ι → ι) → ι . x7 (λ x11 . 0) 0 (λ x11 . 0)) (λ x9 . λ x10 : ι → ι . x10 0) 0 0)) (λ x8 . Inj0 x8) 0 x6 ...) ....