His statement, “if it is effected using the wording of divorce”: for example, he says to his wife, “I divorce you in return for compensation amounting to such-and-such.”
His statement, “or with the intention of divorce”: that is, the husband intends divorce by this separation; in that case, it takes effect as a revocable divorce.
This is the view adopted by the author, based on the position that if khulʿ is effected using the wording of divorce, it constitutes a divorce. The correct view, however, is that nothing takes effect—neither divorce nor khulʿ. As for khulʿ not taking effect, that is because there is no compensation; and as for divorce not taking effect, that is because khulʿ is not a divorce, even if it is effected using the wording of divorce.