
899 A.2d 632 (2006)
95 Conn.App. 670
Anthony HOPKINS
v.
COMMISSIONER OF CORRECTION.
No. 26123.
Appellate Court of Connecticut.
Argued March 28, 2006.
Decided May 30, 2006.
*633 Thomas P. Mullaney III, special public defender, for the appellant (petitioner).
Frederick W. Fawcett, supervisory assistant state's attorney, with whom, on the brief, was Jonathan C. Benedict, state's attorney, for the appellee (respondent).
FLYNN, C.J., and ROGERS and LAVINE, Js.
FLYNN, C.J.
The petitioner, Anthony Hopkins, appeals from the judgment of the habeas court dismissing his third amended petition for a writ of habeas corpus. The court granted the petitioner's request for certification to appeal. On appeal, the petitioner first asks this court to decide whether "the burden of proof in habeas cases [should] be modified in matters where the petitioner presents credible evidence of an available alibi witness to shift the relative burden of proof back to the State thereby requiring the State to offer clear and convincing evidence to overcome a presumption that trial counsel's decision was ineffective, and that [the] petitioner's defense was thereby prejudiced." As an intermediate appellate court, we are bound by Supreme Court precedent and are unable to modify it, as the petitioner's counsel has conceded. As we have explained previously: "We are not at liberty to overrule or discard the decisions of our Supreme Court. . . ." (Internal quotation marks omitted.) State v. Colon, 71 Conn.App. 217, 245-46, 800 A.2d 1268, cert. denied, 261 Conn. 934, 806 A.2d 1067 (2002). Accordingly, we decline to address further that aspect of the petitioner's appeal. Additionally, the petitioner claims on appeal that his trial counsel, Frank J. Riccio, provided ineffective assistance because he failed to interview and to present an additional alibi witness at trial. We disagree and affirm the judgment of the habeas court dismissing the habeas petition.
Prior to discussing the factual and procedural history relevant to our disposition of the petitioner's appeal, we set forth the standard by which we review the habeas court's factual findings. "[I]n a habeas action in which the petitioner alleges ineffective assistance of trial counsel, the underlying historical facts found by the *634 habeas court may not be disturbed unless they were clearly erroneous. . . ." (Internal quotation marks omitted.) Ledbetter v. Commissioner of Correction, 275 Conn. 451, 453 n. 1, 880 A.2d 160 (2005), cert. denied sub nom. Ledbetter v. Lantz, ___ U.S. ___, 126 S.Ct. 1368, 164 L.Ed.2d 77 (2006). "[M]ixed questions of fact and law, which require the application of a legal standard to the historical-fact determinations, [however] are not facts in this sense. . . . Whether the representation a defendant received . . . was constitutionally inadequate is a mixed question of law and fact.... As such, that question requires plenary review by this court unfettered by the clearly erroneous standard." (Citations omitted; internal quotation marks omitted.) Copas v. Commissioner of Correction, 234 Conn. 139, 152-53, 662 A.2d 718 (1995).
As the United States Supreme Court explained in Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), proof of an ineffective assistance of counsel claim requires the petitioner to demonstrate: (1) that counsel's performance was deficient and (2) that the deficient performance prejudiced the defense. "A claim of ineffective assistance of counsel consists of two components: a performance prong and a prejudice prong. To satisfy the performance prong, a claimant must demonstrate that counsel made errors so serious that counsel was not functioning as the counsel guaranteed . . . by the Sixth Amendment.... To satisfy the prejudice prong, a claimant must demonstrate that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different.... The claim will succeed only if both prongs are satisfied." Ledbetter v. Commissioner of Correction, supra, 275 Conn. at 458, 880 A.2d 160, citing Strickland v. Washington, supra, at 687, 694, 104 S.Ct. 2052.
The habeas court set forth the following procedural history, which is not in dispute. On July 28, 1989, the petitioner was convicted of felony murder, assault in the first degree and attempt to commit robbery in the first degree, and was sentenced to a total effective term of fifty years imprisonment. His conviction was upheld on direct appeal. See State v. Hopkins, 222 Conn. 117, 609 A.2d 236 (1992). In 1994, the petitioner filed a petition for a writ of habeas corpus alleging that Riccio had been ineffective in several respects. This petition was denied on June 25, 1996, and the judgment was affirmed by this court. See Hopkins v. Commissioner of Correction, 47 Conn.App. 910, 701 A.2d 355, cert. denied, 243 Conn. 956, 704 A.2d 804 (1997). The petitioner was represented by attorney Michael Moscowitz on that petition. The petitioner then filed a petition for a writ of habeas corpus in the United States District Court for the District of Connecticut. That petition was denied by the District Court, the denial was affirmed by the United States Court of Appeals for the Second Circuit on September 6, 2001, and a petition for a writ of certiorari was denied by the United States Supreme Court on April 15, 2002.
The petitioner filed the original habeas petition in the present case on December 6, 1999, with the third amended petition being heard on September 30, October 21 and October 22, 2003. The petitioner made several claims with respect to Riccio that the habeas court deemed abandoned. The only claims related to the ineffectiveness of trial counsel that were briefed adequately alleged that Riccio did not properly investigate or present the petitioner's alibi defense. The petitioner also claimed that his first habeas counsel, Moscowitz, was ineffective because "he failed to fully investigate and follow-up on leads to alibi and exculpatory witnesses that were available to testify in 1989 at the *635 criminal trial and in 1996 at the first habeas trial." The habeas court rejected these claims and dismissed the petitioner's third amended habeas petition. This appeal followed.
On appeal, the petitioner claims that Riccio provided ineffective assistance in that he did not investigate or present the petitioner's alibi defense properly.[1] We do not agree.
At the petitioner's criminal trial, alibi testimony was presented from Robert Johnson on the petitioner's behalf. Johnson testified that he and the petitioner were in New York with two women, Arlene Speller and her sister, at the time the crimes at issue were committed. Johnson also testified that Speller was his girlfriend. During the habeas trial, Riccio testified that he had thought Johnson would present himself as a credible witness and, therefore, he did not consider using either of the two women to bolster Johnson's testimony or the alibi defense. On appeal, the petitioner asserts only that Speller's testimony should have been introduced at his criminal trial. The petitioner argues in his appellate brief that he "presented additional independent alibi testimony from an additional witness, Arlene Speller, at the habeas trial . . . [and that] [t]his evidence, if offered to and credited by the original trial jury, would have been cumulative evidence tending to raise doubt as to the petitioner's presence at the crime scene at the date and time of the commission of the crimes." (Citation omitted.)
During the habeas proceeding, Speller testified that she was with Johnson and the petitioner on August 26, 1988, and that she specifically remembered being with them on that particular date because it was near her son's birthday. She could not remember, however, what she did on August 26 in subsequent years. Additionally, Speller testified that she had not heard from Johnson or the petitioner after August 26, 1988, and that she had not heard about the crimes until a few weeks before the habeas hearing when an investigator telephoned her. When questioned by the investigator, she did not immediately remember Johnson or the petitioner, but she later telephoned the investigator when she had some recall. No evidence or testimony was presented that Speller had been available to testify at the petitioner's criminal trial, and the petitioner conceded in his habeas brief that her availability merely was "speculative." On the basis of these facts and the partial trial transcript submitted to the habeas court, the court concluded that the petitioner had failed to prove that Riccio's decision not to call additional alibi witnesses was anything more than "sound trial strategy." The court also found that the petitioner had failed to prove that he was prejudiced by Riccio's decision not to call additional alibi witnesses.
"[T]here is a strong presumption that the trial strategy employed by a criminal defendant's counsel is reasonable and is a result of the exercise of professional judgment...." (Citation omitted.) Iovieno v. Commissioner of Correction, 67 Conn.App. 126, 128, 786 A.2d 1113 (2001), cert. denied, 259 Conn. 916, 792 A.2d 851 (2002). "In consideration of [a] petitioner's claim concerning the adequacy of trial counsel's investigation and the calling of *636 alibi witnesses, [t]he petitioner seeks to have us use hindsight with [regard] to his counsel's decision not to call the witnesses to testify. We will not do so. We have stated that the presentation of testimonial evidence is a matter of trial strategy. . . . The failure of defense counsel to call a potential defense witness does not constitute ineffective assistance unless there is some showing that the testimony would have been helpful in establishing the asserted defense." (Internal quotation marks omitted.) Dunkley v. Commissioner of Correction, 73 Conn.App. 819, 823-24, 810 A.2d 281 (2002), cert. denied, 262 Conn. 953, 818 A.2d 780 (2003).
In this case, we agree with the habeas court that the petitioner failed to demonstrate that Riccio's decision not to call Speller as an additional alibi witness was anything more than sound trial strategy. Riccio was an exceptionally experienced criminal defense attorney, having tried fifty-five criminal cases to conclusion in the four or five years preceding the petitioner's 1989 criminal trial, and we will not second-guess his strategy without some showing that Speller's testimony would have been helpful to the petitioner's defense. The petitioner, however, has made no showing that the testimony of Speller would have been helpful in establishing his defense. As a matter of fact, there was no testimonial or documentary evidence submitted to the habeas court that would even establish that she was available to testify at the petitioner's criminal trial. "In a habeas corpus proceeding, the petitioner's burden of proving that a fundamental unfairness had been done is not met by speculation but by demonstrable realities." Ostolaza v. Warden, 26 Conn.App. 758, 765, 603 A.2d 768, cert. denied, 222 Conn. 906, 608 A.2d 692 (1992). We simply find no merit to the petitioner's claim.
The judgment is affirmed.
In this opinion the other judges concurred.
NOTES
[1]  At the habeas trial, the petitioner also claimed that Riccio was ineffective because he did not interview Raymond Jeffries, a person also implicated in the crimes for which the petitioner had been charged. The petitioner has not briefed this issue on appeal. Additionally, at the habeas trial, the petitioner had claimed that his first habeas counsel provided ineffective assistance. This claim also has not been briefed on appeal. Accordingly, we deem those aspects of the habeas petition abandoned.
