This appeal requires our interpretation of the differentiating elements of the crimes of burglary and criminal trespass. We find the difference between the two crimes is the intent involved and the nature of the property entered. Although the jury which convicted defendant of attempted burglary was not properly instructed on the intent element of criminal trespass, the defendant was not prejudiced as a result, and we affirm the trial court.
An attendant at a Des Moines video arcade, Chris Burson, sat down to eat with friends at the arcade at 1:00 a.m. April 29, 1984. The business was closed to the public. At 1:45 a.m. Burson heard the alarm sound at the rear of the fire door and when he went to inspect, found the defendant, Duane Phillips, entering the back door. Burson grabbed the defendant and notified police. Burson testified Phillips kept saying “don’t turn me in.” Burson also said the defendant first said he was hungry and wanted some food, then said he wanted money, and finally said he needed money for a fix. When the police arrived, Phillips told the arresting officer he entered the door because it was open. He later told an investigating detective that he had been *317leaning against the door while urinating, that the door pushed in and someone grabbed him. At trial he said he urinated behind the building and, while waiting for his ride to return, was struck in the back, grabbed, and pulled inside the building. An inspection of the scene by police revealed no evidence of urination, fresh pry marks on the rear fire door, and a crow bar within a few feet of the door. Opinion testimony was offered by the State that the rear door had been pried open.
The defendant was charged with second-degree burglary. At the close of evidence, he objected to the wording in the instruction on the lesser included offense of criminal trespass. Instruction numbers 10 and 11 informed the jury that among the elements of criminal trespass, they would need to find that the defendant entered with the intention of committing a theft.
The defendant says this is error, since the distinguishing feature of burglary and the lesser included trespass offense is the intent. He argues the intent to commit a theft must be found for burglary to occur, but intent to commit a public offense is all that is required of the trespass violation. The State claims the difference between the crimes is the type of property involved. It says the property involved in a burglary must not be open to the public, where with trespass it does not matter if the property is open to the public or not.
The supreme court has discussed the elements of each offense in State v. Sangster, 299 N.W.2d 661, 664 (Iowa 1980) where it determined that criminal trespass was a lesser included offense of burglary. A burglary occurs when three elements are proven. The first element is the intent to commit a felony, assault, or theft. Id. at 662; Iowa Code § 713.1 (1985). The second proof that must be made is that the defendant had no right, license or privilege to do the act. Id. The last element is fulfilled by proving one of three alternatives. Id. The wording of the statute has been modified from the Sangster case somewhat, but is the same for the purposes of this appeal.1 The State can show the defendant; (1) entered an occupied structure which was not open to the public, or (2) remained therein after the right, license or privilege to be there has expired, or (3) broke an occupied structure. Iowa Code § 713.1 (1985). A review of the statute shows that it is possible to commit burglary on public property. This occurs when the first two elements are met, and there is proof the person remained in an area after their right to be there has expired. There is nothing in the statute limiting the property involved to private property. The nature of the property as public or private cannot be the distinguishing factor.
Instead, the court revealed two distinctions between the crimes. The first is that the property upon which a burglary occurs must be “occupied” as defined in the code. Id. The property entered upon pursuant to the criminal trespass statute does not have to be occupied or be a building for keeping something of value. Id. at § 716.7(2)(a).
The second difference between the crimes is the intent required for each. This was made clear by the court in Sangster when it said:
Although the intent elements differ, the intent for criminal trespass is a constituent of the intent element in burglary. The trespass offense merely requires an intent to commit a public offense whereas the burglary offense requires an intent to commit a particular kind of public offense, “a felony, assault or theft.”
Sangster, at 664. (emphasis added). The case shows that the intent to commit a public offense includes theft, and other types of public offense. Therefore, the *318trial court here was in error when it did not tell the jury that if it found the defendant had the intent to commit a public offense, he would be guilty of criminal trespass.
The State argues in the alternative there is no prejudice to the defendant by any error committed. It claims the only conclusion that may be reached by the jury is that either the defendant was guilty of burglary or he was not guilty at all. The State continues that there is no proof in the evidence which might have allowed the jury to find the defendant guilty of criminal trespass.
A finding of error below is insufficient alone to warrant reversal of a conviction, prejudice to the defendant must also occur. State v. Cole, 295 N.W.2d 29, 40 (Iowa 1980). However, prejudice is presumed where there is error unless the contrary is shown. State v. Henze, 356 N.W.2d 538, 540 (Iowa 1984). Error is also presumed where an erroneous instruction is given to the jury. State v. Davis, 228 N.W.2d 67, 73 (Iowa 1975).
We have determined that legally, the instruction on the lesser included offense of criminal trespass should have been included. However, as the State points out, there is no prejudice to the defendant if factually there is no basis for submitting an instruction on trespass. A lesser offense is factually included in the greater offense if there is sufficient evidence in the record which would justify a jury finding the lesser offense was committed. State v. Harlow, 325 N.W.2d 90, 91 (Iowa 1982); State v. Morgan, 322 N.W.2d 68, 70 (Iowa 1982).
We agree with the State that there is no factual basis in this case to warrant submitting the trespass instruction to the jury. The defendant’s claims that he was hungry and wanted food, wanted money, and needed money for a fix all go to the intent to commit a theft by taking “possession or control of the property of another, or property in the possession of another, with the intent to deprive the other thereof.” Iowa Code § 714.1 (1985). The defendant’s statement that he walked through the door because it was open would not support the intent to commit a public offense. It has been stated that if a person does not enter for one of the proscribed purposes as set out in the trespass statute, there is no violation of criminal law until the person refuses to leave after being requested to do so. 43 Op.Att’y Gen. 317 (1979). The other statements by the defendant that he fell or was pushed into the door negate any intent and show only an unintentional entry into the building. The fact the building was occupied is not disputed in this appeal. Even if any one of the stories of defendant was believed, the jury would either find the defendant committed a burglary, or was not guilty. In such a situation the included offense instruction need not be given. State v. Harlow, at 91; State v. Morgan, at 79. The defendant was not prejudiced by the error of the court and we affirm his conviction.
AFFIRMED.
. The Code in effect at the time of Sangster indicated the property must be occupied or enclosed to provide a place for keeping valuable property. Sangster, at 664; Iowa Code § 713.1 (1979). The newest version refers only to an "occupied structure” and defines an occupied structure elsewhere as including a building used to keep something of value. Iowa Code §§ 713.1, 702.12 (1985).