A more thorough explanation:

The Declaration of Independence is a formal proclamation made on July 4, 1776, by the American colonies. It declared their independence from the British Crown and announced themselves as an independent nation to the world.

A declaration of legitimacy is a statement asserting the legitimacy of something or someone. For example, a government may issue a declaration of legitimacy to assert its authority and legitimacy to its citizens and the world.

A declaration of no defenses is also known as a waiver of defenses. It is a legal document in which a defendant waives their right to raise certain defenses in a lawsuit. For example, a defendant may waive their right to claim that the statute of limitations has expired.

A declaration of pain is a statement made by a patient to describe their level of pain. For example, a patient may say "I am experiencing severe pain" to their doctor to help them diagnose and treat their condition.

The Declaration of Paris is an international agreement signed by several European countries in 1856. It declared that privateering is illegal and that a neutral flag covers an enemy's goods, except for contraband. This agreement helped establish rules for maritime warfare and protect neutral countries during times of war.

These examples illustrate how the term "declaration" can be used in different contexts, from legal documents to international agreements to medical statements. Declarations are often used to assert or establish something, whether it is a country's independence or a patient's level of pain.