intros h M N K L.
unfold irreducible in |- *.
unfold reduce in |- *.
tauto.
Qed.

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).