You are the head of the legal department $($general counsel$)$ for a large online private retail corporation, Nomorbunk. The Chief Executive Officer $($CEO$)$ of Nomorbunk $($Lida$)$ is an avid supporter of former President Trump. Lida instructs all employees that they must not post or share any negative opinions about former President Trump in any online forum or social media platform. Lida further informs all employees that any violation of this policy can result in their being fired. The next month Lida instructs Human Relations $($HR$)$ to fire an employee $($Gretchen$)$ who violated Lida's instructions $--$ that is$,$ after Lida's warning Gretchen still retweeted a negative comment about former President Trump on Twitter using her iPhone. HR is hesitant to fire Gretchen because they are concerned about Gretchen's First Amendment right to share her opinions about President Trump through her personal Twitter account. HR has come to you for advice about whether it's legally permissible for the CEO $($Lida$)$ to fire Gretchen in light of the First Amendment.

True or False: As general counsel, you correctly explained that Lida or Nomorbunk did not violate Gretchen's First Amendment rights.