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As for the lineages you listed as being at Shaolin Bodhidharma's lineage is usually considered to have died out with the sixth patriarch (if he existed). Between the mid 9th century and the early 10th century the five schools of Chan came into existence. During the time between then and the mid 13th century when Xueting Fuyu became abbot, what lineages of Chan were practiced at the temple?
Are you suggesting that when a patriarch dies without naming another, their entire teaching is forgotten and lost in the world? There was no seventh patriarch because it was unnecessary. Chan had become well-rooted and flourished by that point.