Answer:
1. Writ requiring a person be brought to court --- Habeas corpus
2. Facts which prove that a crime has been committed --- Corpus delicti
3. Written sworn testimony --- Deposition
4. Writ issued by a high court to a lower court --- Mandamus
5. Investigation before a judge --- Hearing
6. Rehearing in a higher court --- Appeal
Step-by-step explanation:
1- Habeas Corpus is the legal procedure by which any citizen can appear immediately before the judge to determine the legality of the arrest.
2- By corpus delicti should be understood the set of objective elements that constitute the materiality of the criminal figure, that is, the elements that demonstrate the existence of a crime.
3- A deposition is a document in which a witness records a statement outside the court for the purpose of trial.
4- Mandamus is an extraordinary legal remedy where a superior court orders a subordinate court, company, or public authority to do or not to do a specific act that is not entirely private.
5- In law, a hearing is a procedure before a court or other official decision-making body, such as a government agency or other public body (such as the Parliament or Government).
6- The appeal is a means of judicial challenge through which seeks a higher court to amend the resolution of the lower court.