If the lesser offense has a broader array of possible facts, it is possible that the lesser offense is a lesser included offense of the greater, but the greater is not a greater inclusory offense of the lesser.

That is, one who commits 120.08 always commits 120.05(3), but it is not the case that every commission of 120.05(3) is elevated to 120.08 if the injury is a serious physical injury instead of mere physical injury. That is because the categories of victims under 120.05(3) have been broadened to include, "medical or related personnel in a hospital emergency department", a class of victims not specified in 120.08.

Therefore, 120.08 lists 120.05(3) as a lesser included offense, but 120.05(3) does not list 120.08 as a greater inclusory offense.

On the other hand, if the greater offense has a broader set of possible facts, it will be possible to commit the greater without committing the lesser offense. In this case, the lesser offense is not a legal lesser included offense. However, the greater offense still may be considered a greater inclusory offense with respect to the lesser offense. For example,

§ 175.35 (Offering a false instrument for filing in the first degree) is committed when a person,

"knowing that a written instrument contains a false statement or false information, and with intent to defraud the state or any political subdivision, public authority or public benefit corporation of the state, he offers or presents it to a public office, public servant, public authority or public benefit corporation with the knowledge or belief that it will be filed with, registered or recorded in or otherwise become a part of the records of such public office, public servant, public authority or public benefit corporation."

The lesser offense of 170.30 (OFIFF2d degree), is committed when a person,

"knowing that a written instrument contains a false statement or false information, he offers or presents it to a public office or public servant with the knowledge or belief that it will be filed with, registered or recorded in or otherwise become a part of the records of such public office or public servant."

Thus, if the intent to defraud is added to 170.30, the greater offense of 175.35 results. However, one who intends to defraud a "public authority" by his conduct commits 175.35 but not 175.30. Consequently, 175.30 is no longer a legal lesser included of 175.35, although 175.35 may still be considered a greater inclusory offense with respect to 175.30.