How did rebellions in the Americas and Europe reflect Enlightenment ideas?

All of the revolutions in the Americas and Europe reflect Enlightenment ideas, as can be seen in the documents proclaiming independence. The U.S.'s "Declaration of Independence" emphasized the inalienable rights to life, liberty, and pursuit of happiness--almost verbatim from Enlightenment thinker John Locke's ideas. Also, the "Declaration of Independence" stated that Britain's monarchy had become tyrannical which therefore justified their rebellion. This aligns with Locke's reasoning that if a government failed to fulfill its promises to its citizens, it ceased to be authentic and could be superseded. The French "Declaration of the Rights of Man and of the Citizen" gave citizenship to people who were not just of the aristocracy. Along with that citizenship, it  guaranteed the basic rights of free speech, ownership of property, and protection from arbitrary acts of the state. Finally, the revolution in Haiti strongly reflects the new Enlightenment thought that blacks were, in fact, not inferior to whites. The blacks and mulattoes in Haiti were fed up with always being second to whites, even when the people of color were free plantation owners. After a number of successful slave revolts, France granted independence to slaves in Haiti.

For more information on the Haitian Revolution, watch the video below: