Is a previous divorce considered following a new marriage contract?

If a woman returns to her husband with a new marriage contract after her divorce, she returns with two remaining divorces. This is by agreement of the scholars if she did not marry someone else after her divorcer. An undivorced woman (who has not been consummated with) becomes irrevocably separated with one divorce. If her divorcer wishes for her, he can marry her with a new marriage contract, and she returns to him with two remaining divorces. If he divorces her twice and then marries her, she returns to him with one remaining divorce.