Definition IfEq b l1 l2 := L.equal cmp l1 l2 = b.

Lemma cons_IfEq : forall b x1 x2 d1 d2 l1 l2, X.eq x1 x2 -> cmp d1 d2 = true -> IfEq b l1 l2 -> IfEq b ((x1,d1)::l1) ((x2,d2)::l2).