delivered the opinion of the court:
Defendant, Paul Lynch, Sr., was charged with murder in the circuit court of Lake County. The defense was self-defense, and defendant was convicted of voluntary manslaughter. Defendant appealed, and this court affirmed in an unpublished order. (People v. Lynch (1983), 117 Ill. App. 3d 1162, 466 N.E.2d 417; see 87 Ill. 2d R.23.) The Illinois Supreme Court granted leave to appeal, reversed the conviction, and remanded for a new trial. (People v. Lynch (1984), 104 Ill. 2d 194, 470 N.E.2d 1018.) Defendant was retried for voluntary manslaughter and was again convicted. This appeal is from that conviction.
The facts adduced at defendant’s second trial were essentially the same as those adduced at his first trial. Since those facts are summarized in the supreme court’s opinion (People v. Lynch (1984), *990104 Ill. 2d 194, 198-99, 470 N.E.2d 1018, 1019-20), they will not be repeated here. Additional facts necessary to the resolution of the issues raised will be noted in the discussion of the issues to which they relate.
Defendant raises several issues on appeal. He argues that he was not proved guilty beyond a reasonable doubt of voluntary manslaughter, in that the evidence was insufficient to establish that defendant caused the death of Lester Howard (the victim) and that defendant was not acting in self defense. He also argues that the trial court erred in denying a motion for substitution of the judge; admitting into evidence the bloody coat of Howard; failing to follow the supreme court’s mandate by refusing to admit into evidence three battery convictions of Howard; and refusing to admit evidence of Howard’s alcohol level. Finally, defendant argues that various omissions on the part of defense counsel deprived him of his constitutional right to the effective assistance of counsel. We reverse and remand for a new trial.
Defendant’s challenges to the sufficiency of the evidence ■will be addressed first. Throughout a criminal trial, the burden of proving beyond a reasonable doubt all of the material and essential elements constituting a crime is on the prosecution. (People v. Weinstein (1966), 35 Ill. 2d 467, 469-70, 220 N.E.2d 432, 433-34.) The function of the trier of fact is to determine the credibility of witnesses, the weight to be given their testimony, and the inferences to be drawn from the evidence. (People v. Akis (1976), 63 Ill. 2d 296, 298, 347 N.E.2d 733, 734.) The function of this court in reviewing the sufficiency of the evidence on which defendant was convicted is to carefully review the evidence, giving due consideration to the fact that the trial court and jury saw and heard the witnesses. (People v. Jefferson (1962), 24 Ill. 2d 398, 402, 182 N.E.2d 1, 2.) The evidence adduced in the case at bar was sufficient to permit the jury to conclude that defendant’s guilt of voluntary manslaughter had been established beyond a reasonable doubt.
Defendant’s first argument in this regard, that proof that defendant caused Howard’s death was insufficient, borders on the frivolous. The evidence established that Howard was apparently fine before defendant shot him, that defendant shot him, and that he then immediately collapsed to the floor. The paramedic who first treated Howard saw a hole in his head which appeared to be a gunshot wound. The autopsy, performed the day after Howard was shot, showed that Howard died of a gunshot wound to the head.
Defendant’s claim is that the evidence does not establish beyond *991a reasonable doubt that the gunshot wound which killed Howard was inflicted by defendant. He argues that no one saw “blood pouring from Howard’s head” after defendant shot Howard, and that the only evidence of the presence of blood was the blood found on Howard’s jacket which, defendant maintains, suggests that defendant shot Howard in the body rather than the head. It is apparently defendant’s theory that the fatal head wound could have been inflicted by someone else after defendant shot Howard. This theory is a completely original creation on appeal, since defendant never contested his having caused Howard’s death at trial. Moreover, there was no evidence of any wound other than the fatal head wound (there being no reason why the blood on the jacket could not have come from the head and no testimony that there was any other wound). Under the circumstances, the jury was certainly justified in concluding that the evidence proved beyond a reasonable doubt that defendant caused Howard’s death by shooting him in the head. Indeed, a contrary conclusion would have been unreasonable.
Defendant also argues that the evidence that he was not acting in self-defense was insufficient. The relevant statute provides:
“A person is justified in the use of force against another when and to the extent that he reasonably believes that such conduct is necessary to defend himself or another against such other’s imminent use of unlawful force. However, he is justified in the use of force which is intended or likely to cause death or great bodily harm only if he reasonably believes that such force is necessary to prevent imminent death or great bodily harm to himself or another, or the commission of a forcible felony.” (Ill. Rev. Stat. 1983, ch.38, par. 7 — 1.)
There is no question that defendant believed it was necessary to shoot Howard to prevent imminent death or great bodily harm to himself. It is the sufficiency of the evidence that defendant’s belief was unreasonable which is at issue.
The reasonableness of defendant’s belief was a matter for the jury to decide. (People v. Johnson (1954), 2 Ill. 2d 165, 171-72, 117 N.E.2d 91, 95; see also People v. Lockett (1980), 82 Ill. 2d 546, 553, 413 N.E.2d 378, 381-82 (including statement that “[w]e can conceive of no circumstance when a judge could determine, as a matter of law, that a jury could find the defendant had a reasonable subjective belief the killing was justified, but that the jury could not find the defendant’s subjective belief was unreasonable”).) The jury in the case at bar concluded that defendant’s belief that killing Howard was justified was unreasonable.
*992The evidence established that Howard and his friend Ernest Bell were in the apartment of defendant’s son, Paul Lynch, Jr. (Paul, Jr.), to discuss payment of money Paul, Jr., owed Bell for taking and wrecking Bell’s car. Bell and Howard were at the apartment when defendant arrived. Paul, Jr., was disabled physically and mentally as a result of brain surgery. Bell and Howard were younger and much larger than defendant, both being in their thirties and about 6 feet 4 inches, 230 pounds. The testimony of the three persons who witnessed the shooting differed somewhat. Paul, Jr., testified that Howard “started to make a move toward *** [defendant] with his hands on the side so I could see.” Bell testified Howard may have made one or two steps toward defendant and that Howard’s hands at the time he was shot were in front of him. Defendant testified that Howard moved toward him quickly and reached under his jacket behind his back. No one testified that they saw a weapon in Howard’s possession or that they subsequently found a weapon.
As can be seen, the evidence on this question was close. The jury could reasonably have inferred that the State had failed to disprove self-defense beyond a reasonable doubt. However, the jury could also reasonably infer, as it did, that the evidence established beyond a reasonable doubt that it was unreasonable for defendant to believe it was necessary to shoot Howard to prevent his own imminent death or great bodily harm. The evidence was therefore sufficient to sustain the jury’s finding that defendant committed voluntary manslaughter.
Defendant next contends that he did not receive a fair trial because the trial court erroneously admitted Howard’s bloody coat into evidence, failed to admit evidence of Howard’s blood alcohol level, denied a motion for substitution of judges, and failed to admit into evidence three convictions of Howard for battery which were the subject of the supreme court’s opinion reversing and remanding the case for a new trial. The bloody coat’s admission was not objected to at trial or in the post-trial motion. (People v. Lucas (1981), 88 Ill. 2d 245, 250, 430 N.E.2d 1091, 1093; People v. Dixon (1967), 37 Ill. 2d 416, 226 N.E.2d 608, cert. denied (1967), 389 U.S. 871, 19 L. Ed. 2d 150, 88 S. Ct. 153.) The denial of the motion to substitute judges (which asserted an absolute right to substitution and was not based on actual prejudice) was not raised in the post-trial motion. (See People v. Thomas (1978), 58 Ill. App. 3d 460, 461-62, 374 N.E.2d 795, 797; see also People v. Jones (1974), 24 Ill. App. 3d 1052, 1056, 322 N.E.2d 579, 581; People v. Spencer (1972), 7 Ill. App. 3d 1017, 1023, 288 N.E.2d 612, 616.) The error claimed with *993respect to evidence of Howard’s blood-alcohol level is asserted in defendant’s brief without citation to any authority supporting its admission. (103 Ill. 2d R. 341(e)(7); In re Marriage of Anderson (1985), 130 Ill. App. 3d 684, 688-89, 474 N.E.2d 911, 914; see also People v. Ramirez (1983), 98 Ill. 2d 439, 472, 457 N.E.2d 31, 47 (supreme court declined to address issue in a capital case because appellant failed to comply with Rule 341(e)(7).) These three grounds for defendant’s claim that his trial was unfair have accordingly been waived.
The other ground on which defendant claims his trial was unfair is that the trial court refused to admit three battery convictions of Howard in contravention of the supreme court’s opinion reversing and remanding this case. (See People v. Lynch (1984), 104 Ill. 2d 194, 470 N.E.2d 1018.) This issue was properly preserved in the trial court and has been at least adequately argued in defendant’s brief. It will therefore be addressed.
The evidence which the trial court refused to admit was certified copies of three battery convictions of Howard under a municipal ordinance. There is no question that these were the convictions which were the subject of the prior appeal in this case. The supreme court reversed defendant’s conviction and remanded for a new trial on the ground that the three battery convictions of Howard were admissible and the trial court erroneously refused to admit them into evidence. People v. Lynch (1984), 104 Ill. 2d 194, 202, 204-05, 470 N.E.2d 1018, 1021, 1022 (“In this case, therefore, Howard’s convictions were admissible for the purpose of proving that he was the aggressor.” “The batteries were competent evidence to prove that Howard was an aggressive and violent man.” “It was reversible error to exclude evidence that Howard had three battery convictions”).
The controlling principles are old ones — often referred to as the law-of-the-case doctrine — which promote judicial economy by putting an end to the litigation of issues once they have been finally decided by a higher court. As the Illinois Supreme Court said many years ago:
“After a judgment is reversed and the cause is remanded the inferior tribunal can take only such further proceedings as conform to the judgment of the appellate tribunal. If specific directions are given nothing can be done except carry out those directions. If no specific directions are given it must be determined from the nature of the case what further proceedings will be proper and not inconsistent with the opinion. It is not required that specific directions shall be stated in an order *994reversing a judgment and remanding a cause, and it is the duty of the court to which the cause is remanded to examine the opinion and proceed in conformity with the views expressed in it. For the purpose of determining what proceedings the court may take in conformity with the views expressed in the opinion it is necessary to ascertain what the issues are and to examine the opinion of the court which deals with them. [Citations.]” (Roggenbuck v. Breuhaus (1928), 330 Ill. 294, 297-98, 161 N.E. 780, 781-82.)
See People ex rel. Horberg v. Waite (1909), 243 Ill. 156, 160-61, 90 N.E. 183, 185-86; People v. Webb (1982), 109 Ill. App. 3d 328, 331, 440 N.E.2d 406, 407.) The issue at bar concerns the admissibility of evidence, which is a question of law. (People v. Brannon (1978), 59 Ill. App. 3d 531, 533, 375 N.E.2d 840, 841.) Questions of law decided in a prior appeal of a case are binding on both the trial and appellate courts. (People ex rel. Kastning v. Militzer (1921), 301 Ill. 284, 287, 133 N.E. 761, 762; Zokoych v. Spalding (1980), 84 Ill. App. 3d 661, 667, 405 N.E.2d 1220, 1226.) A necessary corollary to this is that on remand a trial court must proceed in accordance with an appellate court’s decision, even if the appellate court applied an erroneous rule of law. Baum v. Hartmann (1909), 238 Ill. 519, 87 N.E. 334.
The mandate in the case at bar was general in its terms. An examination of the opinion of the supreme court reveals that a question of law which was necessary to the decision was whether the three battery convictions of Howard were admissible. The supreme court decided that they were, and so reversed and remanded for a new trial because the trial court had excluded them. On remand, the trial court should have admitted them, but instead permitted the State to relitigate the admissibility of the convictions, albeit on somewhat different grounds. In this the trial court erred.
The State resists this conclusion on the basis that the evidence of the batteries by Howard was unreliable and “there were no ‘convictions’ in the sense of the term as used in” the supreme court’s opinion. This does not explain why the trial court on remand, or this court on this appeal, would have the authority to hold inadmissible evidence the supreme court held admissible. Moreover, the premises on which the State’s argument is based are questionable.
The basic premises underlying the State’s argument are that the supreme court did not realize that the batteries (or at least two of them) were disposed of by ex parte judgments against Howard or that they were municipal ordinance rather than State statute viola*995tions. It is by no means clear that this is true.
The trial court concluded, we think correctly, that the supreme court apparently had a rap sheet for Howard in its possession when it decided defendant’s first appeal. (See People v. Lynch (1984), 104 Ill. 2d 194, 203, 470 N.E.2d 1018, 1021.) The rap sheet in the record clearly shows that two of the battery judgments against Howard were ex parte. Therefore, either the supreme court did not find the ex parte nature of the judgments significant or the State waived any claim that this makes the evidence inadmissible by not raising it in the prior appeal. See, e.g., Kazubowski v. Kazubowski (1970), 45 Ill. 2d 405, 413, 259 N.E.2d 282, 288, cert. denied (1970), 400 U.S. 926, 27 L. Ed. 2d 186, 91 S. Ct. 188.
The other premise of the State’s argument is that the supreme court’s use of the word “conviction” did not encompass adjudications of guilt for ordinance violations. Here, too, the rap sheet reference to “ex parte” militates against the State, since an adjudication of guilt of violation of a criminal statute in this State would not be made “ex parte.” A criminal defendant could be tried “in absentia”; however, that would involve an actual trial and not the entry of ex parte judgment. (See Ill. Rev. Stat. 1985, ch. 38, par. 115 — 4.1; Black’s Law Dictionary 517 (5th ed. 1979) (definitions of “ex parte,” “ex parte hearing,” and “ex parte proceeding”).) Thus the reference to two of the battery judgments as ex parte was indicative to the court and parties that they were not for violations of a State statute.
There is also nothing about the use of the word “conviction” which excludes municipal ordinance violations. Although there are instances when the term is used in the restricted sense the State would assign to it in this case (see, e.g., Ill. Rev. Stat. 1985, ch. 38, pars. 2 — 5, 2 — 12, 2 — 22), the word is commonly used to refer to adjudications of guilt of ordinance violations (see, e.g., Ill. Rev. Stat. 1985, ch. 38, pars. 1005-1-5, 1005-1-15; People v. Stout (1968), 41 Ill. 2d 292, 293, 242 N.E.2d 264, 265 (wherein supreme court said defendant was “convicted of violating a ‘disorderly conduct’ ordinance and a ‘fast driving’ ordinance” and the court characterized one of the issues raised as a charge “that the evidence was insufficient to sustain the convictions for ‘disorderly conduct’ and ‘fast driving’ ”).) Since there is no indication in the supreme court’s opinion in the case at bar that the word “conviction” was being used in the narrow sense urged by the State, and there is an indication that the record before the supreme court would at least have suggested that the batteries at issue were ordinance violations, the State’s *996claim that ordinance violation convictions are not encompassed by the supreme court’s use of the term “conviction” is questionable.
The State’s argument is based on its belief that the supreme court did not have all of the information it needed to determine the admissibility of Howard’s convictions. The supreme court addressed the question of whether it had sufficient information in disposing of a contention of the State on the first appeal that the issue of the admissibility of the convictions had been waived by the failure of defendant to make an offer of proof. The court said:
“The State’s argument is that we do not know enough about the facts of Howard’s batteries to tell whether they were the sort that demonstrate general aggressive propensities. ***
The evidence here was to be elicited from Bell, the State’s chief witness, and the initial knowledge the defense gained about the convictions came from the State’s discovery answer. The State therefore knew as much about the facts as the defense, unless the defendant had made an investigation on his own. In these circumstances, at least, we should not demand that the record provide exhaustive detail; it is enough if, from the record before us, we can say with confidence that the proffered evidence should have been admitted. This is not a case of an attorney disclosing a misleading selection of facts, hoping to slip into evidence a conviction that, were all the facts known, would clearly be inadmissible.
In general, battery is prima facie probative enough of aggressive and violent tendencies to be admissible. The rap sheets included in the State’s discovery answer show that all three convictions were recent, the last coming only six weeks before the homicide; all were in Illinois, so there is no problem of a strange definition of battery in another jurisdiction. If the State believed that there was nevertheless something so peculiar about the batteries as to make them inadmissible, the State could have asked for further details from defense counsel, or investigated them itself, or questioned Bell, the State’s witness, about the details he knew. However, the State did not do that. Nor did it mention that any necessary details of the batteries were missing at any time in the circuit court, although the issue of their exclusion on the ground that defendant was unaware of them at the time of the homicide was extensively briefed and argued on the post-trial motion. The State’s complaint that there should have been an offer of *997proof is an afterthought, and wholly academic.” (People v. Lynch (1984), 104 Ill. 2d 194, 202-04, 470 N.E.2d 1018, 1021-22.)
The supreme court was thus confident that it knew enough about the batteries to determine they were admissible. We will not second guess this conclusion of the court.
Thus, the supreme court’s mandate required that Howard’s convictions for battery be admitted into evidence. Moreover, the State has not established that the supreme court did not understand the nature of the convictions or that, even if the court did misunderstand, the State did not waive its claim during the prior appeal. Thus, the circuit court’s judgment must again be reversed and the cause remanded for a new trial.
The final issue raised by defendant is whether he was denied the effective assistance of counsel. All but one of the claimed errors of counsel concern his conduct at trial. Since this case is being reversed and remanded for other reasons, it is unnecessary to consider whether the claimed trial errors of counsel constituted ineffective assistance of counsel.
The remaining claimed error is that “[djefense counsel failed to be prepared to present precedent to the Court to support the motion for substitution of judge (R. 373).” The record citation is to a part of defense counsel’s closing argument to the jury and so does not support the claimed error of not presenting precedent to support the pretrial motion for substitution of judges. This sentence is the only part of defendant’s ineffective-assistance-of-counsel argument concerning this particular claimed error, so there is no other record citation to support it. Because defendant has not cited to us any part of the record supportive of this claim, we will not consider it. 103 Ill. 2d R. 341(e)(7); People v. Ramirez (1983), 98 Ill. 2d 439, 472, 457 N.E.2d 31, 47 (supreme court declined to address allegation of ineffective assistance of counsel in a capital case where allegation did not comply with Rule 341(e)(7)).
The judgment of the circuit court of Lake County is accordingly reversed, and the cause is remanded for a new trial.
Reversed and remanded.
DUNN and WOODWARD, JJ., concur.