The State of Michigan appeals the judgment of the United States District Court for the Eastern District of Michigan conditionally granting Robert Mathis (“Mathis”) a writ of habeas corpus. Because we find that there is a reasonable probability that the result of the trial would have been different if the evidence Mathis learned of after the trial had been disclosed in time for him to present it to the jury, we affirm the district court’s judgment.

I.

This case arises from the alleged rape of Betty Hawthorne (“Hawthorne”) by Mathis and David Mockbee (“Mockbee”). Hawthorne testified at trial that she and her friend Michelle Martin (“Martin”) met Mathis and Mockbee at Jumpin Jack’s bar on the evening of August 25, 1994. According to Hawthorne, after Martin left the bar, Hawthorne followed Mathis to his home believing that Martin had gone there with one of Mathis’s friends. Hawthorne arrived at Mathis’s home at approximately 2:30 a.m., but Martin was not there. Hawthorne testified that when she attempted to leave, she was knocked to the floor by Mathis and another man. Hawthorne said that one of the men knelt on her arms for about half an hour, pinning her to the floor, and during that time she was vaginally raped by the men and forced to perform fellatio on them. She claimed that she left the house crying, and that the two men followed her out to her car. Although Hawthorne testified that the men touched her car, the fingerprints lifted from the car by police did not match those of Mathis or Mockbee.

Hawthorne called the police after she got home at approximately 4:00 a.m. The report of Officer Nelson, who interviewed Hawthorne that night, states that Hawthorne identified one of her assailants as a dark-haired man with the possible name of “Mike.” The next day, after speaking with Mathis’s next door neighbor (who told her that Mathis’s name was “Bob”), she identified her alleged attacker to Officer Novak as “Bob” and changed her descriptions as to hair color.

Following her initial meeting with Officer Nelson. Hawthorne went to the hospital where she was examined and a rape kit was prepared. The examination produced no physical evidence of rape or any evidence of ejaculation. Despite Hawthorne’s claim that a man had knelt on her arms for *103over 30 minutes, the examining doctor found no evidence of bruising other than a leg bruise that was approximately one day old.

In addition to Hawthorne’s testimony, the state introduced the testimony of Mathis’s neighbor, James Colpaert, and Colpaert’s 11-year-old daughter. Colp-aert testified that he saw Mathis and Mockbee arrive at Mathis’s house at about 2:30 a.m., followed soon by Hawthorne in a separate car. He said that Hawthorne left the house crying and hysterical approximately 45 minutes later, saying “you shouldn’t have done it.” Colpaert’s daughter testified that she was looking out the window with her father, and saw a girl in a car crying and a man standing by her car door.

Mathis testified at trial that he and Mockbee were at Jumping Jack’s on the night in question until 2:30 a.m. He claims that he did not go home that evening, but rather went to his mother’s home. He denied knowing Hawthorne.

A jury found Mathis guilty of two counts of criminal sexual misconduct. Following the guilty verdict, Mathis discovered that Hawthorne had filed a number of police reports prior to the one underlying his conviction. Two of these reports are of particular interest: they involve highly dubious — if not patently false — allegations that she was a victim of violent crimes including rape and armed robbery. The new evidence obtained by Mathis forms the heart of this dispute, and is described at length by Judge Gadola in his opinion granting a writ of habeas corpus:

After trial, Petitioner learned of the evidence upon which he bases his Brady argument. This evidence consists of two police reports detailing previous complaints that the complainant made to police....

The first of these reports is from 1988 and involves a complaint of rape that the complainant made to the City of Warren Police Department. The police report relates the following information. The complainant told police that, early on August, 27, 1988. a man forced her into his auto, drove her to the rear of a factory parking lot, and committed acts of battery and rape that culminated in the attacker’s ejaculation. The alleged attacker then released the complainant, who proceeded to look for her boyfriend. When she found her boyfriend several hours later, the two of them went to his house and went to sleep.

After the complainant awoke, she contacted police and described the above events. Police interviewed her and the complainant then selected a “mug shot” of a man who looked similar to the man who allegedly raped her.

A physician’s examination was conducted on the complainant on the same day of the alleged attack, as was a rape kit. The physician’s examination returned “negative results. ” The rape kit indicated that there was “no evidence of semen” because “the swab was not used from the rape Mt.” Police also collected the clothing that the complainant wore on the day of the alleged rape, but that evidence also did not show evidence of semen.

On August 29, 1988. the detective assigned to the case spoke with the manager of the factory whose parking lot allegedly was where the rape occurred. That manager revealed that “the gates [to the parking lot] were closed and locked promptly at 18:30 hours on Friday, August, 26, and that it would have been impossible for a car to drive to the rear of the factory without unlocking those gates as [the complainant] had reported. Further, [the detective] personally examined said gates on the date *104of the occurrence [August 27] and again on the 29th of August and determined that there was no visible sign of any forced entry or damage to the gate or lock.”

On August 31, 1988 the complainant had an appointment with the detective, but “failed to appear,” claiming that she could not get a ride to the police station. The detective told the complainant to arrange for transportation and a new appointment would be set. From that date until September 26. the complainant and detective exchanged telephone messages but were not able to set an interview time.

. Finally, on September 26, 1988. the complainant called and arranged an interview with the detective for September 28. The detective’s entry from September 28 is as follows:

[The complainant] appeared this date and looked at several additional photographs of possible suspects in this matter with negative results. [The complainant] did indicate that she saw a vehicle and suspect matching the description of the alleged rapist in this matter in the area of Eight Mile and Gratiot on Monday, 9-26, at approximately 01:30 Hrs. She indicated there was no license plate on the car and that the friends that she was with would not follow the car to determine its destination or to attempt to identify the driver.

In addition it should be noted that [the complainant] failed to bring this information to my attention until nearly 48 hours later at our interview. [The complainant] was advised that she appeared to be disinterested in the investigation and further that if there were no further leads in the very near future, that the case would be closed. [The complainant] seemed to be quite indifferent with [sic] this information and the interview was terminated....

The second police report to which Petitioner points is from 1992 and involves the complainant’s assertion that she was the victim of an armed robbery. This police report revealed that the complainant stated that, while she was walking in an alley near her home, a man produced a gun, threatened to kill her, and demanded her leather jacket. According to the complainant, the robber took her jacket and she dropped a package as she ran from him. The pregnant part of the investigating officer’s report is as follows:

After I cleared the seen [sic] I returned to the alley where [the complainant] stated she had been robbed. Snow was fresh and I felt the suspect could have left foot prints which would have been valuable evidence. Investigation did in fact show foot prints in the fresh snow. I found the prints to be small and appeared to be a womens [sic] print. I located no other prints in the snow. These prints were so fresh I could read the writing from the sole of the shoe in the snow which stated “The Winner”. These prints led to the rear of a Michigan Bell transmitter where I found [the complainant’s] coat and package had been placed. There were no other footprints and I’m sure the suspects would have left prints. It appeared [the complainant] had placed the items behind the box, because I noticed entrance and exit prints .... we returned to [the complainant’s] home to question her further about the robbery. I read Miranda Warnings via card and [the complainant] stated she understood the rights and was willing to speak with us. [The com*105plainant] stated she was telling the truth, but became very nervous. I asked to see the soles of the shoes she was wearing and they were the same shoe with “The Winner” stamped across the bottom.

(Emphasis added and footnotes omitted.)

The officer’s robbery report also reflects that at a second interview, Hawthorne asked, “what could happen to me” in response to the officer’s statement that she would be charged with making a false police report if in fact she was falsifying a report.

Mathis moved for a new trial, claiming that this evidence from prior police reports was impeachment evidence that the prosecutor had been required to turn over to Mathis under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). The trial court denied the motion for new trial. The Michigan Court of Appeals affirmed, and the Michigan Supreme Court denied discretionary review. Mathis then filed this habeas action pursuant to 28 U.S.C. § 2254. Based on the new evidence and the rule established in Brady, Judge Gadola issued a writ of habeas corpus ordering a new trial or release. This appeal followed.

II.

Because Mathis filed his federal petition for writ of habeas corpus after the effective date of The Antiterrorism and Effective Death Penalty Act (“AEDPA”), Pub. L. No. 104-132, 110 Stat. 1214 (Apr. 26, 1996), that statute governs this court’s inquiry. Lindh v. Murphy, 521 U.S. 320, 326-27, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). Under AEDPA’s provisions, a federal court may not grant a writ of habeas corpus with respect to any claim adjudicated on the merits in state court unless such state adjudication:

(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or

(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.

28 U.S.C. § 2254(d)(1).

A state court adjudication is “contrary to” Supreme Court precedent under § 2254(d)(1). “if the state court arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law.” or “if the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent” and arrives at a different result. Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court adjudication involves “an unreasonable application of’ Supreme Court precedent under § 2254(d)(2). “if the state court identifies the correct governing legal rule from [the Supreme] Court’s cases but unreasonably applies it to the facts of the particular ... case,” or if the court unreasonably refuses to extend, or unreasonably extends, existing legal principles from the Court’s precedents to a new context. Id. at 407. The state court’s application must be more than incorrect or erroneous; it must be “objectively unreasonable.” Id. at 409.

The state courts’ factual determinations are to be presumed to be correct-a presumption which the applicant may rebut by clear and convincing evidence. 28 U.S.C. § 2254(e)(1). We review a district court’s disposition of a habeas corpus petition de novo. Bronaugh v. Ohio, 235 F.3d 280, 282 (6th Cir. 2000).

There is no question that the Supreme Court precedent governing Mathis’s petition is Brady v. Maryland and its *106progeny. Under Brady, “suppression by the prosecution of evidence favorable to an accused ... violates due process where the evidence is material, either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution.” Brady, 373 U.S. at 87. The Supreme Court has held that “[t]here are three components of a true Brady violation: The evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently: and prejudice must have ensued.” Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). Prejudice (and materiality) is established by showing that “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Id. at 281 (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)).

One would expect that the State, in ■prosecuting a habeas appeal, would point us to those elements of the State courts’ decisions which are reasonable applications of, or consistent with, relevant United States Supreme Court precedent in order to preclude the issuance of a writ under AEDPA. But the State has not done so. Although identifying Brady and its progeny — including Strickler — as the governing legal rule, the State has not examined the state courts’ opinions in light of that precedent. Rather, the State has quoted — without comment-sections of the state courts’ opinions that are clearly contrary to, or unreasonable applications of. United States Supreme Court precedent, or are simply inapposite to the Brady claim being pressed by Mathis. For example, the State quotes the Macomb County Circuit Court’s 1996 finding that “a new trial will not ordinarily be granted because of newly discovered evidence to impeach a witness.” The case which the Macomb County Court cites for this proposition is Michigan v. Stricklin, 162 Mich.App. 623, 413 N.W.2d 457, 462 (1987), stating that “newly discovered evidence is not grounds for a new trial where it would be used merely for impeachment purposes.” It is entirely unclear to us whether the Macomb County Circuit Court addressed that finding to evidence withheld by the State. If it did, then that statement of law is contrary to clearly established Supreme Court precedent. See Bagley, 473 U.S. at 676 (“Impeachment evidence, however, as well as exculpatory evidence, falls within the Brady rule.”). If it did not, then the statement of law is simply inapposite to Mathis’s claim, and denial of the claim on that basis would be an unreasonable application of clearly established Supreme Court precedent.

The State then quotes at length, but discusses not at all, the 1998 Michigan Court of Appeals decision denying a new trial. In addition to repeating the trial court’s erroneous conclusion that impeachment evidence is not grounds for a new trial, the court found Mathis’s argument to be meritless because “[t]he prosecutor is required to provide any known exculpatory information or evidence to the defense .... Here, there is no indication that the prosecutor was aware of the unrelated police reports at the time of the trial.... ” This is clearly contrary to Supreme Court precedent. See Kyles v. Whitley, 514 U.S. 419, 438, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (stating that Brady’s disclosure requirement encompasses evidence “known only to police investigators and not to the prosecutor”).

After quoting the various state court decisions, the State recites the evidence presented at trial, and concludes that “Mathis has not established that he was denied evidence that, if known, would have resulted in a different verdict,” because *107there was “substantial other evidence of his guilt,” and the undisclosed reports were not material to Mathis’s defense because he failed to prove that the reports made by Hawthorne to the police were false. Notably, despite its failure to acknowledge the state courts’ unreasonable conclusions with regard to the first two prongs of Stickler's three part test, the State does not appear to dispute that Mathis has established those first two prongs; that is, that the police reports would be impeachment evidence and favorable to Mathis, and that those reports were withheld by the State.

The State argues that Mathis cannot demonstrate Stickler’s third prong because he fails to establish prejudice. In particular, Michigan says that Mathis’s “argument that he would have been exonerated of this rape had the jury only known of Hawthorne’s past complaints is conjecture and should not be elevated to fact.” The State, however, entirely misstates the clearly established standard, which requires only a “reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Bagley, 473 U.S. at 682.

Applying the proper prejudice standard, we first must assess whether the evidence is admissible. It clearly is. While Michigan has a rape-shield statute, this law does not preclude admission of evidence of prior false or unsubstantiated rape allegations. See Michigan v. Garvie, 148 Mich.App. 444, 384 N.W.2d 796, 798 (1986) (“Notwithstanding the [Michigan rape-shield] statute, the defendant should be permitted to show that the complainant has made false accusations of rape in the past.”) (internal quotation and citation omitted). And while Michigan does not generally permit the introduction of extrinsic evidence to attack the credibility of a witness, specific instances of conduct may be inquired into on cross-examination of the witness if the court considers them to be probative of truthfulness or untruthfulness. See MRE 608(b). Where, as here, there is no physical evidence supporting the prosecution’s case, the truthfulness or lack of truthfulness of the complainant is a matter of crucial importance.

Michigan’s key argument seems to be that “Mathis offered no proof that the prior allegations were false; therefore, the evidence is not material to his defense and he cannot establish that he was denied a fair trial by the failure to admit the reports.” However, the proof of the falsity or potential falsity of the prior allegations is evident from the face of the reports themselves. Given the inconsistencies in the reports and the impossibility of certain claims made in them, Judge Gadola was correct in finding that “a reasonable jury probably would conclude that the complainant had lied to police about the alleged 1988 rape and the alleged 1992 armed robbery.”

Finally, the government states that Mathis has not established that the admission of this evidence would have resulted in a different verdict “because there was other substantial evidence of his guilt.” This is plainly not the case. First, as we have already noted, Mathis is not required to demonstrate that the admission of this evidence would have resulted in a different verdict, but only that there is a reasonable probability that, had he had this evidence, the result of the proceeding would have been different. See Bagley, 473 U.S. at 682. And secondly, as we have already noted, there is no physical evidence supporting the prosecution’s case. Other than Hawthorne’s account, the only evidence proffered by the prosecution was the testimony of Mathis’s neighbor that Mathis and Hawthorne arrived separately at Mathis’s house in the early morning hours, and that Hawthorne left the house crying and say*108ing “you shouldn’t have done it,” and the testimony of the neighbor’s young daughter that she saw a girl in a car, crying, and a man standing by the car. While this testimony may establish that Hawthorne met Mathis at his house — and thereby contradict Mathis’s testimony that he did not return to his home that evening — such evidence by itself does not establish a crime. Accordingly, because Hawthorne is the only witness to-and, indeed, her testimony is the only evidence of-the alleged crime, her credibility is critical to the prosecution’s — not to mention Mathis’s — case. Under these circumstances, had the jury been aware of this impeaching evidence, “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Bagley, 473 U.S. at 682.

III.

For the foregoing reasons, we AFFIRM the judgment of the district court.