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

Lemma irreducible_op : forall (h : hedge) (oM oN : op) (M N : Msg), irreducible h (Mop oM M) (Mop oN N) <-> analysis_def h (Mop oM M) (Mop oN N) /\ (oM <> oN \/ ~ synthesis (analysis_def h) M N).