
595 F.3d 1245 (2010)
James L. GREEN, Petitioner-Appellant,
v.
Cynthia NELSON, Respondent-Appellee.
No. 08-11212.
United States Court of Appeals, Eleventh Circuit.
February 4, 2010.
*1247 Zachary D. Tripp, King & Spalding, LLP, Washington, DC, Courtland L. Reichman (Court-Appointed), King Spalding, Atlanta, GA, for Green.
Amy E. Hawkin Morelli, Atlanta, GA, for Nelson.
Before TJOFLAT and BARKETT, Circuit Judges, and BARZILAY,[*] Judge.
BARKETT, Circuit Judge:
James L. Green, a Georgia state prisoner serving two consecutive life sentences, appeals the district court's denial of his pro se 28 U.S.C. § 2254 habeas petition in which he raised numerous challenges to his state convictions of rape, aggravated sodomy, and related charges which arose out of two separate attacks on two women. We granted a Certificate of Appealability on the following issues:
Was the state court's determination that Green's trial counsel was not ineffective for failing to file a motion to suppress blood and DNA evidence contrary to or an unreasonable application of clearly established federal law or an unreasonable determination of the facts in light of the evidence presented?
Was the state court's determination that there was sufficient evidence to sustain a conviction for aggravated sodomy as charged in Count Three of the indictment contrary to or an unreasonable application of clearly established federal law or an unreasonable determination of the facts in light of the evidence presented?

*1248 Did the district court err in denying as unexhausted and procedurally barred Grounds Fourteen and Fifteen in Green's federal habeas petition?
Our review of Green's federal habeas petition is governed by the standards set forth in 28 U.S.C. § 2254, as amended by the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"). Green argues, first, that his state convictions must be reversed because of the ineffectiveness of his trial counsel in failing to move to suppress his blood and DNA evidence. Second, he argues that his conviction for aggravated sodomy under Count Three must be reversed because of the complete lack of evidence to support that conviction. He asserts that the state courts unreasonably applied clearly established federal law in rejecting these two claims. Finally, he argues that the district court erroneously determined that Grounds Fourteen and Fifteen of his federal habeas petition were procedurally barred. We address, in turn, each of Green's arguments and the appropriate standard of review under AEDPA for each of these claims.

I.

INEFFECTIVE ASSISTANCE OF COUNSEL
Green argues that his trial counsel was ineffective for not moving to suppress his blood and DNA evidence. The state obtained that evidence with a warrant based on an affidavit containing incorrect statements of fact. Green contends that the affiant knew or should have known that statements in the affidavit were false. The state courts rejected this claim on the merits. Accordingly, § 2254(d) allows us to grant federal habeas relief only if the state court 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).
The Supreme Court has explained that a decision "contrary to" federal law contradicts that Court on a settled question of law or holds differently than did that Court on a set of materially indistinguishable facts. Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). In short, it is a decision "substantially different from the [Supreme Court's] relevant precedent . . . ." Id. A decision that unreasonably applies federal law identifies the correct governing legal principle as articulated by the United States Supreme Court, but unreasonably applies that principle to the facts of the petitioner's case. Id. at 407. In other words, it is one that "unreasonably extends [the] principle . . . to a new context where it should not apply or unreasonably refuses to extend [it] to a new context where it should apply." Id. Finally, "a decision adjudicated on the merits in a state court and based on a factual determination will not be overturned on factual grounds unless objectively unreasonable in light of the evidence presented in the state-court proceeding. . . ." Miller-El v. Cockrell, 537 U.S. 322, 340, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
Here, we look to the decision by the Court of Appeals of Georgia on Green's direct appeal in Green v. State, 249 Ga.App. 546, 547 S.E.2d 569 (2001), because the state habeas court concluded that it was bound by the state appellate court's decision regarding the merits of *1249 this claim.[1] The state court's findings and conclusion relevant to the ineffective assistance of counsel claim are as follows:
Finally, Green argues ineffective assistance because his counsel did not file a motion to suppress evidence of a blood sample taken from Green. In his appellate brief, Green raises concerns regarding the lawfulness of the warrant for the blood sample and argues that his counsel should have moved to suppress that evidence.
Again, Green's claim of ineffective assistance of counsel fails. The decision of whether to file a motion to suppress is a matter of professional judgment, and we will not judge counsel's trial strategy in hindsight.
Although another lawyer may have conducted the defense in a different manner and taken another course of action, the fact that defendant and his present counsel disagree with the decisions made by trial counsel does not require a finding that defendant's original representation was inadequate.
Counsel's decisions on matters of tactic and strategy, even if unwise, do not amount to ineffective assistance of counsel.
Green, 249 Ga.App. at 554, 547 S.E.2d 569 (internal citations and quotation marks omitted).
Ineffective assistance of counsel claims are governed by the standard set forth by the Supreme Court in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). "An ineffective assistance claim has two components: A petitioner must show that counsel's performance was deficient, and that the deficiency prejudiced the defense." Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (citing Strickland, 466 U.S. at 687, 104 S.Ct. 2052). To establish deficiency, a defendant must show that "counsel's representation `fell below an objective standard of reasonableness.'" Wiggins, 539 U.S. at 521, 123 S.Ct. 2527 (quoting Strickland, 466 U.S. at 688, 104 S.Ct. 2052). The Supreme Court instructs that the standard for appropriate attorney conduct is one of "reasonableness under prevailing professional norms." Id. "[S]trategic choices made after less than complete investigation are reasonable precisely to the extent that reasonable professional judgments support the limitations on investigation." Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052. A failure to file a motion to suppress that is based on a lack of knowledge of the state of the evidence due to counsel's misunderstanding or ignorance of the law or failure to conduct adequate investigations can satisfy Strickland's deficiency prong. Kimmelman v. Morrison, 477 U.S. 365, 383-87, 106 S.Ct. 2574, 91 L.Ed.2d 305 (1986). Additionally, to establish prejudice, a defendant must prove "a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland, 466 U.S. at 694, 104 S.Ct. 2052.
The evidence relating to Green's claim that he received ineffective assistance *1250 of trial counsel is as follows: Green was convicted of rape, sodomy, assault, and other charges that involved two victims and took place at two different times. The first victim, Sylvia Grisson, testified that she was attacked in her home by a man, later identified as Green, who forced her to perform oral sex on him and to lick his anus. He then pushed her down on her bed and raped her. The man also ejaculated. Grisson immediately called the police, who came to her home and took her to the hospital where a rape kit was performed. Grisson never identified Green as her attacker and did not testify to any other details of the crime.
The second victim, Beverly Pollard, was also attacked in her home by Green about two months after Grisson's attack. Green threatened her with a gun and stated that this was not the first trailer he had broken into. He forced her to remove her clothing and then placed his mouth on her vagina and also inserted his penis into her. After a struggle for Green's gun, Green ran out of the trailer. When the police arrived, Pollard, who recognized Green because they lived in the same trailer park, gave a description of him to the officers who subsequently located Green and took him into custody.
Detective Sheree Tovey testified that Pollard identified Green as her rapist and told her that Green had admitted that he had been in other trailers in the park. Tovey then executed an affidavit to obtain a search warrant for Green's bodily fluids. In her affidavit, Detective Tovey attested that Pollard had been "forced to engage in vaginal intercourse with James L. Green" and also that "[a]s a result of this intercourse, a deposit of semen was collected from the body of Beverly Pollard." The affidavit further provided that "Deponent believes that the blood of James L. Green can be proven to have the unique DNA make up of that in the semen collected from the body of Beverly Pollard." Tovey's two statements in her affidavit that semen was collected from Pollard were incorrect. The lab report on Pollard's rape kit, dated one month after the search warrant for Green's blood and DNA evidence was issued, indicated that there were no spermatozoa or seminal fluid on the swabs taken from Pollard.
Green was tried and convicted at the same trial for the attacks on both Grisson and Pollard. Although Grisson was not able to identify Green as her attacker, the State implicated Green for the attack on Grisson with the evidence of Green's blood and DNA, which had been obtained as a result of the search warrant issued in the investigation of Pollard's attack.
Green moved for a new trial, in part because of his trial counsel's failure to move to suppress evidence of his blood and DNA. At the evidentiary hearing on Green's motion for a new trial, his trial counsel testified that he reviewed the affidavit in support of the search warrant for Green's blood and the lab report on Pollard's rape kit. He agreed that he should have moved to suppress the blood and DNA evidence but did not do so because he "obviously misread the Affidavit as to which victim was which." He then responded that the failure to file a motion to suppress was "absolutely not" a conscious decision on his part, with full knowledge of the case file. The trial court denied the motion. Green raised this claim again on direct appeal and in his state habeas proceedings. The state appellate court considered and rejected this claim on the merits, concluding that Green's trial counsel had made a strategic decision, and the state habeas court also rejected the claim, acknowledging that it was bound by the appellate court's decision.
*1251 Green argues that the facts surrounding his trial counsel's failure to move to suppress the blood and DNA evidence clearly demonstrate that his trial counsel did not make a choice in this regard, let alone a strategic choice. In particular, Green argues that his trial counsel's performance was deficient because the decision not to pursue a suppression motion was based on his trial counsel's mistaken understanding to which victim the affidavit was referencing. This obvious mistake had the potential to disadvantage Green because the only evidence connecting him to the rape of the first victim, Sylvia Grisson, was the blood and DNA evidence obtained through the allegedly fraudulent warrant.
We agree with Green that there is no basis in this record to conclude that his trial counsel made a strategic decision not to file a motion to suppress. The evidentiary record shows that Green's trial counsel's failure to file a motion to suppress was not the result of a strategic decision-making process but rather of inaction resulting from an admittedly mistaken view of the evidence in the case.
The state court's contrary determination that Green's counsel made a strategic choice was based on the erroneous assumption that the decision whether to file a motion to suppress is always a matter of strategy.[2] However, the Supreme Court has explained that decisions that are based on mistaken beliefs certainly are neither strategic nor tactical. See Kimmelman, 477 U.S. at 383-87, 106 S.Ct. 2574. Rather, strategic decisions are ones that, among other things, involve a weighing of competing positive and negative consequences that may flow to the defendant from a particular choice. Here, filing a motion to suppress could have had no possible negative impact on Green's defense and, if granted, would have almost assuredly precluded his conviction. The failure to file a motion to suppress was not tactical; it was deficient performance and the state court's determination to the contrary was "an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d). Accordingly, we owe no AEDPA deference to the state appellate court's unreasonable determination and must review the performance prong of Green's ineffective assistance claim de novo. Wiggins, 539 U.S. at 528-34, 123 S.Ct. 2527. Under this standard, for the reasons expressed above, we find that the failure of Green's trial counsel to move to suppress the blood and DNA evidence constitutes deficient performance.
We next turn to Strickland's second prong of an ineffective assistance of counsel claimwhether "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." 466 U.S. at 694, 104 S.Ct. 2052. Because the state appellate court found Green's trial counsel's performance adequate it did not address Strickland's prejudice element and so we evaluate this element de novo. See Rompilla v. Beard, 545 U.S. 374, 390, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005).
To establish prejudice in the context of ineffective assistance of counsel for failure to raise a Fourth Amendment claim, a defendant must show that (1) the underlying Fourth Amendment issue has merit and (2) there is a "reasonable probability that the verdict would have been different absent the excludable evidence *1252. . . ." Kimmelman, 477 U.S. at 375, 106 S.Ct. 2574. When challenging the integrity of a warrant under the Fourth Amendment, a defendant must make a substantial showing of a "deliberate falsehood or reckless disregard for the truth," in the affidavit supporting the issuance of the warrant. Franks v. Delaware, 438 U.S. 154, 171, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978). If that standard is met, the affidavit should be examined with the incorrect assertions set aside to determine if the remaining information is sufficient to establish probable cause. Id. at 171-72, 98 S.Ct. 2674.
Green urges us to remand his case for an evidentiary hearing under Franks to determine whether the warrant issued to obtain his blood and DNA violated his Fourth Amendment rights. We decline to do so, however, because there is ample evidence in the record to resolve this issue. Even if we presume, without deciding, that in her affidavit Detective Tovey deliberately falsified or recklessly disregarded the truth of the fact that no semen was collected from Pollard, we must still examine the affidavit without the false information to determine whether the remaining information would have been enough to establish probable cause. Id. The factually accurate information in the affidavit is as follows:
Deponent believes that James L. Green. . . has committed the act of Rape, against one, Beverly Pollard . . . . Investigation reveals that said Beverly Pollard, describes that during these sexual acts, she was forced to engage in vaginal intercourse with James L. Green. . . . Further investigation led to the positive identification of James L. Green, by Beverly Pollard, and his subsequent arrest.
None of these statements are challenged by Green as being false and indeed, Pollard provided this information to the investigating law enforcement officers and testified to these facts at trial. She also identified Green as her attacker upon her initial report of the rape and attack to the police. Considering the affidavit with these facts onlyincluding that Green raped Pollard and that Pollard positively identified Green as her attackerwe find probable cause existed to obtain a search warrant for Green's blood and DNA evidence. See Maryland v. Pringle, 540 U.S. 366, 370-71, 124 S.Ct. 795, 157 L.Ed.2d 769 (2003) (explaining that the probable cause standard is a "practical, nontechnical conception that deals with the factual and practical considerations of everyday life on which reasonable and prudent men, not legal technicians, act" and one that provides a "reasonable ground for belief of guilt") (quotation marks omitted).
Accordingly, we find no prejudice stemming from the failure of Green's trial counsel to request the suppression of Green's blood and DNA evidence. We therefore deny his federal habeas petition as it pertains to this claim of ineffective assistance of trial counsel.

II.

AGGRAVATED SODOMY CONVICTION
Green next argues that his conviction on Count Three of the indictment violated his federal due process rights because there was insufficient evidence to support the jury's verdict as required by Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). This count alleged that Green committed aggravated sodomy against the first victim, Sylvia Grisson, by "unlawfully plac[ing] his penis in her anus. . . ." Georgia law provides that aggravated sodomy is "any sexual act involving the sex organs of one person and the mouth or anus of another" that is committed *1253 "with force and against the will of the other person." Ga.Code Ann. § 16-6-2(a). Proof of penetration is not required; some contact is sufficient. Griffis v. State, 222 Ga.App. 322, 323, 474 S.E.2d 119 (1996). Rape is a distinct and separate offense that requires proof of penile-vaginal penetration. Compare Ga.Code Ann. § 16-6-2 with § 16-6-1.
The state appellate court correctly recognized that it must "determine whether the evidence is sufficient under [the Supreme Court's decision in] Jackson v. Virgina" to support a conviction for aggravated sodomy. Green, 249 Ga.App. at 548, 547 S.E.2d 569; see also Estelle v. McGuire, 502 U.S. 62, 68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991) ("In conducting habeas review, a federal court is limited to deciding whether a conviction violated the Constitution, laws, or treaties of the United States."). AEDPA requires that we defer to the state court's decision on this issue, unless we find that it was an unreasonable application of or contrary to Supreme Court precedent or that it involved an unreasonable determination of the facts in light of the evidence presented. 28 U.S.C. § 2254(d).
It is undisputed that the only evidence presented to the jury on the charge of aggravated sodomy was that:
The first victim [Grisson] testified that, while threatening her with a knife, Green forced her to perform oral sex on him and to lick his anus. She further testified: "He pushed me down on the bed and raped me."[3]
Green, 249 Ga.App. at 549, 547 S.E.2d 569. According to the state appellate court, these three sexual acts provided a sufficient basis for a rational juror to infer that contact between Green's penis and Grisson's anus also occurred. We do not agree that such an inference could possibly be drawn from the evidence presented.
In Jackson, the Supreme Court held that a conviction violates federal due process if, viewed in the light most favorable to the prosecution, the evidence is not sufficient for "any rational trier of fact [to] have found the essential elements of the crime beyond a reasonable doubt." 443 U.S. at 319, 99 S.Ct. 2781. In this case, there was no express testimony that Green's penis touched Grisson's anus. Moreover, we cannot conclude that any rational juror could have drawn an inference from the testimony actually presented that the necessary contact occurred.
The state appellate court applied Jackson to conclude that the three acts committed provided a sufficient basis for a rational juror to infer that the charged aggravated sodomy, a crime with separate and distinct elements, occurred. This conclusion, and the inference on which it is based, is an unreasonable application of Jackson on this record. The factual elements necessary for proof of aggravated sodomy in the form of penile-anal contact cannot be inferred from either the penile-oral contact, or the penile-vaginal penetration, or the oral-anal contact which did occur. There is no basis for any rational juror to conclude otherwise.
Accordingly, the state appellate court unreasonably applied Jackson's sufficiency of the evidence standard, and we grant Green's petition requesting the reversal of his conviction for aggravated sodomy of Grisson as charged in Count Three.


*1254 III.

PROCEDURAL BAR AS TO GROUNDS FOURTEEN AND FIFTEEN
In Ground Fourteen of his federal habeas petition, Green raised the issue of the validity of the affidavit discussed above. In Ground Fifteen, Green argued that his appellate counsel was ineffective for failing to raise the issue that his trial counsel was allegedly ineffective regarding a motion to sever. The district court concluded that these two claims were procedurally barred, believing that Green failed to raise them at any time prior to his federal habeas petition. The district court was incorrect.
AEDPA requires a petitioner to exhaust remedies available in state court before bringing them in a federal habeas petition. 28 U.S.C. § 2254(b)(1)(A). Whether a claim is exhausted is a mixed question of fact and law which this court reviews de novo. Mauk v. Lanier, 484 F.3d 1352, 1357 n. 3 (11th Cir.2007). The Supreme Court has explained that a petitioner need only "fairly presen[t] federal claims to the state courts in order to give the State the opportunity to pass upon and correct alleged violations of its prisoners' federal rights." Duncan v. Henry, 513 U.S. 364, 365, 115 S.Ct. 887, 130 L.Ed.2d 865 (1995) (quotation marks and citation omitted). When a claim has been so presented to the state courts and denied, that claim is exhausted. See Mauk, 484 F.3d at 1357.
Upon our review of the record it is apparent that Ground Fourteen of Green's federal habeas petition was raised as Ground Nineteen of his state habeas petition. Likewise, Ground Fifteen of his federal habeas petition was previously raised as Ground Three of his state habeas petition. Although the language is not identical in his federal and state habeas petitions, Green made a fair presentment of his claims such that the state court would be able to address their merits.[4]See Duncan, 513 U.S. at 365, 115 S.Ct. 887. Moreover, it is apparent that the state habeas court addressed and denied on the merits Ground Three of his state habeas petition (federal habeas Ground Fifteen). With regard to Ground Nineteen of Green's state habeas petition (federal habeas Ground Fourteen), the state court identified it in its decision, thereby indicating that the state court was adequately notified of this claim. See Mauk, 484 F.3d at 1357.
Thus, as Grounds Fourteen and Fifteen of Green's federal habeas petition were not procedurally barred, we remand them to the district court to decide whether the state court's resolution of these issues involved an unreasonable application of, or was contrary to, clearly established federal law. See Upshaw v. Singletary, 70 F.3d 576, 580 (11th Cir.1995) (remanding claim that was not procedurally barred to the district court for an evidentiary hearing).

CONCLUSION
We AFFIRM the district court's judgment that Green did not receive ineffective assistance of counsel based on his trial counsel's failure to file a motion to suppress; we REVERSE the district court on Green's claim that there was insufficient evidence to sustain his conviction for aggravated *1255 sodomy as charged in Count Three and direct the district court to issue the writ and vacate his conviction and sentence on this count; and we REVERSE the denial of Green's claims in Grounds Fourteen and Fifteen of his federal habeas petition as procedurally barred and REMAND for further proceedings to determine if Green is entitled to relief on these claims.[5]
AFFIRMED, in part; REVERSED, in part; and REMANDED.
NOTES
[*]  Honorable Judith M. Barzilay, Judge, United States Court of International Trade, sitting by designation.
[1]  The district court concluded, in part, that Green's ineffective assistance of counsel claim was procedurally barred from federal habeas review because the state habeas court dismissed it on "independent and adequate state procedural grounds." This conclusion, however, is erroneous. Although the state habeas court did not independently adjudicate the merits of Green's ineffective assistance of trial counsel claim, it did not reach the merits because it believed itself to be bound by the state appellate court's merits-based decision on this issue, which had been presented on direct appeal. The state habeas court's refusal to re-adjudicate this issue on the merits a second time does not bar federal habeas review. See Cone v. Bell, ___ U.S. ___, 129 S.Ct. 1769, 1782, 173 L.Ed.2d 701 (2009).
[2]  The state court held that "[t]he decision of whether to file a motion to suppress is a matter of professional judgment" and that "decisions on matters of tactic and strategy, even if unwise, do not amount to ineffective assistance of counsel." Green, 249 Ga.App. at 554, 547 S.E.2d 569.
[3]  The state also charged Green with aggravated sodomy of Grisson based on the forcible licking of his anus. However in Green's direct appeal, the state court reversed his conviction under this count because the facts as alleged did not constitute aggravated sodomy under Georgia law, which requires penile-anal or penile-oral contact. The state did not charge Green with aggravated sodomy based on the forcible penile-oral contact.
[4]  We also note that at the time Green brought his state habeas petition and filed the original federal habeas petition, he was proceeding pro se. Although we find that Green made a fair presentment of Grounds Fourteen and Fifteen in his state habeas petition as written, we note that pro se pleadings are generally held to a less stringent standard than pleadings drafted by attorneys, and thus should be liberally construed. See Hughes v. Lott, 350 F.3d 1157, 1160 (11th Cir.2003).
[5]  In Green's initial brief filed with this court while he was proceeding pro se, Green also requested that we expand the certificate of appealability ("COA") previously granted by this court to include three claims that we had already considered and rejected in his original request for a COA. The supplemental brief filed by his court-appointed counsel does not include this request or address any of the three additional claims. We find no basis to expand the COA.
