Section Σ11_reduction.
(* We can lower the hypotheses now bu computing m from A *)
Variable (n : nat) (Y : Type) (HY : finite_t Y) (A : fol_form (Σ11 (pos n) Y)) (K : Type).
Let m := lmax (map (@length _) (Σ11_words A)).
Let Hm w : In w (Σ11_words A) -> length w < S m.
Definition Σ11_red := Σfull_mon_red' HY m A.

Theorem Σ11_red_correct : fo_form_fin_dec_SAT_in A K <-> fo_form_fin_dec_SAT_in Σ11_red K.