Let x0 of type ((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 → CT2 ι) → ι → ι → 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 be given.
Assume H0:
∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . 0) (Inj0 (x5 (λ x8 : ι → ι . 0))) (λ x8 : (ι → ι) → ι → ι . λ x9 . x2 (λ x10 . 0) (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 x14 . setsum (x12 0) (x3 (λ x15 x16 . λ x17 : (ι → ι) → ι . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 . 0))) (λ x10 x11 . x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . Inj0 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) 0 (x6 (λ x10 : ι → ι → ι . Inj0 0)) (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . x9) (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 x14 . 0) (λ x10 x11 . 0) 0 0 0 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum 0 0)) (x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . 0) 0)) (λ x10 . x8 (λ x11 . 0) (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . 0) 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 . x9)))) = x2 (λ x8 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . x3 (λ x16 x17 . λ x18 : (ι → ι) → ι . 0) (x1 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 x18 x19 . 0) 0) (λ x16 : (ι → ι) → ι → ι . λ x17 . x2 (λ x18 . 0) 0 (λ x18 . 0))) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . x15) 0)) x8 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0)) (x2 (λ x8 . 0) 0 (λ x8 . x6 (λ x9 : ι → ι → ι . Inj0 x8))) (λ x8 . setsum 0 (x5 (λ x9 : ι → ι . Inj1 (x6 (λ x10 : ι → ι → ι . 0))))).
Assume H1:
∀ x4 x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . 0) (x4 (x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . 0) (x3 (λ x8 x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) x7 (λ x8 : (ι → ι) → ι → ι . λ x9 . x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . 0) 0)) (λ x8 : (ι → ι) → ι → ι . λ x9 . setsum (x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . 0) 0) (x2 (λ x10 . 0) 0 (λ x10 . 0))))) (λ x8 : (ι → ι) → ι → ι . λ x9 . x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . setsum (x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . Inj1 0) (λ x14 x15 . x0 (λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 x20 . 0) (λ x16 x17 . 0) 0 0 0 0) x12 x11 (x3 (λ x14 x15 . λ x16 : (ι → ι) → ι . 0) 0 (λ x14 : (ι → ι) → ι → ι . λ x15 . 0)) (setsum 0 0)) (Inj0 (Inj0 0))) x9) = x4 x7.
Assume H2:
∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x8 . setsum (x7 (x6 (Inj1 0) (λ x9 . x8) (x2 (λ x9 . 0) 0 ...)) ...) ...) ... ... = ....