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Legal proceedings are generally characterized by an orderly process in which participants or their representatives are able to present evidence in support of their claims, and to argue in favor of particular interpretations of the law, after which a judge, jury, or other trier of fact makes a determination of the factual and legal issues. (Wikipedia)

legal proceedings: actions taken to settle an argument in a court of law (Merriam-Webster Dictionary)

Contempt of court is a criminal offence. Contempt can take many forms. The aim of the law is to prevent interference with legal proceedings in the UK. It protects proceedings in all courts and tribunals in the UK which carry out judicial functions. (BBC)

Trump's team pushed to delay legal proceedings at any possible point. (BBC)

Judicial proceedings refer to any legal proceeding carried out in a court of law to determine and enforce legal rights. This can include a variety of legal activities, such as litigation, arbitration, and administrative hearings. (Legal Explanations)

The term “judicial proceedings instituted by the United States” as used in this section refers to all proceedings, whether criminal or civil, including pretrial and grand jury proceedings (as well as proceedings upon a petition for a writ of habeas corpus initiated in the name of the United States by a relator) conducted in, or pursuant to the lawful authority and jurisdiction of a United States district court. (28 USC § 1827(j))