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