Definition good_move (x y : IR) : Prop :=
    (forall k k', ~ (x = IRO k /\ y = IRI k')) /\
    (forall k, ~ (x = IRI k /\ y = IRO k)) /\
    (forall k, ~ (x = IRI k /\ y = IRU k)).

Lemma IR_equiv_Permutation : forall ir1 ir2, IR_equivalent ir1 ir2 -> Permutation ir1 ir2.