(** the irreducibles I(h) of h is (reduce (A(h))) *)
Definition irreducible (h : hedge) := reduce (analysis_def h).

Lemma irreducible_enc : forall (h : hedge) (M N K L : Msg), irreducible h (MEnc M K) (MEnc N L) <-> analysis_def h (MEnc M K) (MEnc N L) /\ (~ synthesis (analysis_def h) M N \/ ~ synthesis (analysis_def h) K L).