An accused may be convicted of a crime included in a crime charged in the indictment or accusation. A crime is so included when:

(1) It is established by proof of the same or less than all the facts or a less culpable mental state than is required to establish the commission of the crime charged; or

(2) It differs from the crime charged only in the respect that a less serious injury or risk of injury to the same person, property, or public interest or a lesser kind of culpability suffices to establish its commission.