Let x0 of type (ι → (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι → ι → ι) → (ι → ι) → ι → ι → (ι → ι) → ι be given.
Let x1 of type (ι → ι) → (CT3 ι) → ι → (ι → ι) → ι be given.
Let x2 of type ((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 → ι → ι be given.
Assume H0:
∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 : ι → ι . 0) x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . 0) (x0 (λ x8 . λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . Inj1 0) x12 (λ x14 . x1 (λ x15 . 0) (λ x15 : ι → ι → ι → ι . 0) 0 (λ x15 . 0))) x10 (λ x13 . x0 (λ x14 . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . x3 (λ x19 : ι → ι . 0) 0 (λ x19 : ι → ι → ι . λ x20 : ι → ι . λ x21 . 0) 0 0) (λ x14 . x13) (x0 (λ x14 . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0) 0 0 (λ x14 . 0)) (setsum 0 0) (λ x14 . setsum 0 0))) (λ x8 . x3 (λ x9 : ι → ι . x3 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0)) (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0 (λ x10 . 0)) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (Inj1 0) (x6 0)) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ι . 0) (Inj0 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 0) (x1 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0) 0 (λ x12 . 0)) (Inj1 0)) 0 x7) (x5 (λ x8 x9 : ι → ι . λ x10 . x9 (x9 0))) x4 (λ x8 . x7)) (x6 0) = x0 (λ x8 . λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . setsum 0 x12) (λ x8 . x1 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . 0) (x1 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . x1 (λ x10 . x9 0 0 0) (λ x10 : ι → ι → ι → ι . 0) (x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . 0)) (λ x10 . x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 (λ x11 . 0))) (x1 (λ x9 . setsum 0 0) (λ x9 : ι → ι → ι → ι . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)) 0 (λ x9 . 0)) (λ x9 . x8)) (λ x9 . x7)) (Inj0 (x2 (λ x8 : ι → ι . x6 (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . 0) (λ x9 . 0) 0 0 (λ x9 . 0))) (λ x8 x9 : (ι → ι) → ι . setsum x7 0))) (setsum (setsum 0 0) x7) (λ x8 . setsum 0 (setsum 0 (setsum (x1 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . 0) 0 (λ x9 . 0)) x7))).
Assume H1:
∀ x4 : (ι → ι → ι → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x8 : ι → ι . x8 (setsum x5 0)) ... ... ... ... = ....