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New York City’s fast-food industry has served as a laboratory for the nation’s labor movement for the last several years.

Its workers were the first to stage rallies demanding a minimum wage of $15 an hour. Then, they pressed for changes in the way national restaurant chains set their work schedules.

Now, they are asking the City Council to shield them from being fired without a valid reason. That protection, the sort of job security that unions usually bargain for, would be a first for a city to provide to workers in a specific industry, labor law experts said.

City Councilman Brad Lander said he planned to introduce a bill on Wednesday that would require fast-food businesses to show “just cause” for firing workers and give them a chance to appeal dismissals through arbitration.