ORDER

Ali Aziz appeals the denial of his motion under 28 U.S.C. § 2254, which alleged that he received ineffective assistance of counsel in the entry of his plea and that his plea lacked a sufficient factual basis. We affirm.

I. Background.

In October 1996 Aziz pleaded guilty to one count of armed robbery pursuant to a plea bargain. During the plea colloquy Milwaukee County Circuit Judge Franke explained the elements of armed robbery, including “that you took ... property by the use or threat of use of an article that was used in a manner that was intended to lead [the victim] to believe that it was a dangerous weapon.” Aziz responded that he understood. Later during the colloquy the court repeated the elements — including that the charge involved use of “an article used or fashioned in a manner to lead [the victim] to reasonably believe that [it] was a dangerous weapon” — and asked Aziz’s attorney, Mr. Rebholz, whether the defense had any material disagreements with the charge. Mr. Rebholz responded that Aziz had not used a weapon but instead a “hand or finger, whatever.” Judge Franke asked Aziz if he had any questions and, after Aziz responded that he did not, asked whether he was pleading guilty to the charge of armed robbery. Aziz pleaded guilty. The court subsequently sentenced Aziz to “an indeterminate period, not to exceed 32 years.”

Aziz moved for post-conviction relief before the trial court and, when that motion was denied, appealed to the Wisconsin Court of Appeals (“Appellate Court”). Aziz claimed that he had received ineffective assistance of counsel because Mr. Re-bholz (1) failed to explain the elements of armed robbery to him, and (2) represented to the trial court that Aziz had put a “hand or finger, whatever” into the victim’s back when — Aziz alleges — he put nothing into the victim’s back. As a result, Aziz alleged, his plea was not knowing and voluntary. Aziz also claimed that his guilty plea lacked a sufficient factual basis. The Appellate Court affirmed. Applying the standards set forth in Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the court concluded that, even if Mr. Rebholz’s performance were deficient, Aziz suffered no prejudice because the record supported the trial court’s findings that Aziz understood the charge against him when he pleaded guilty. The court noted that Judge Franke had explained the elements of armed robbery to Aziz, who acknowledged that he understood. The court also noted that Aziz was present when his counsel made the “hand or finger, whatever” representation and failed to object or attempt to correct the statement. The Appellate Court did not consider Aziz’s sufficiency claim, concluding that Aziz had waived it by failing to raise it in his motion for post-conviction relief. The Wisconsin Supreme Court denied Aziz’s petition for review.

In January 2000 Aziz filed his § 2254 motion, again asserting that he received ineffective assistance of counsel and that his guilty plea lacked a sufficient factual basis. The district court denied the motion as to the ineffective assistance claim but granted a certificate of appealability. The court did not consider the sufficiency claim, concluding that it was procedurally defaulted.

II. Analysis.

On appeal Aziz reasserts his ineffective assistance and sufficiency claims. *613We do not consider Aziz’s sufficiency claim, however, because it was not included in the certificate of appealability. See Ouska v. Cahill-Masching, 246 F.3d 1036, 1045 (7th Cir. 2001). We deny Aziz’s implicit request to amend the certificate to include the sufficiency claim, see id., because the district court correctly determined that it was procedurally defaulted. When Aziz raised his sufficiency claim on direct appeal the Appellate Court concluded based on State v. Giebel, 198 Wis.2d 207, 541 N.W.2d 815, 819 (1995), that Aziz had waived the claim by failing to raise it in his motion for post-conviction relief. The Appellate Court’s conclusion constitutes an independent and adequate state ground for its decision and bars federal review of the sufficiency claim. See Coleman v. Thompson, 501 U.S. 722, 729-30, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991); Franklin v. Gilmore, 188 F.3d 877, 886 (7th Cir. 1999). Aziz alleges no cause for the state procedural default, see Coleman, 501 U.S. at 750, 111 S.Ct. 2546, and did not allege that our refusal to consider his sufficiency claim would work a fundamental miscarriage of justice, see Schlup v. Delo, 513 U.S. 298, 315, 327, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995), until he filed his reply brief on appeal, which is too late, Help At Home Inc. v. Med. Capital, L.L.C., 260 F.3d 748, 753 n. 2 (7th Cir. 2001). We thus limit our review to Aziz’s ineffective assistance claim.

The district court incorrectly reviewed de novo Aziz’s ineffective assistance claim. A petitioner is not entitled to habeas corpus relief under § 2254 unless a state court’s adjudication of the matter “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.” 28 U.S.C. § 2254(d)(1). The phrases “contrary to” and “unreasonable application of’ are independent standards. Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000); Morgan v. Krenke, 232 F.3d 562, 565 (7th Cir. 2000), cert. denied, 532 U.S. 951, 121 S.Ct. 1423, 149 L.Ed.2d 363 (2001).

Aziz does not specify which standard he believes entitles him to relief, but his case does not fit within the “contrary to” standard, which governs only cases where a state court applies the wrong legal rule or confronts facts “materially indistinguishable” from a Supreme Court case but reaches a different result. Williams, 529 U.S. at 405, 120 S.Ct. 1495. The Appellate Court applied the correct legal rule in relying on Strickland, see Hill v. Lockhart, 474 U.S. 52, 57-58, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985) (holding that the Strickland standard applies in the guilty plea context), and Aziz does not contend that the facts of his case are materially indistinguishable from any Supreme Court case.

Neither is Aziz entitled to habeas corpus relief under the “unreasonable application” standard. When a trial court explains the elements of the charge and the consequences of pleading guilty and the defendant acknowledges that he understands, the defendant has suffered no prejudice as a result of deficient performance by counsel in connection with the guilty plea. See Steward v. Gilmore, 80 F.3d 1205, 1212 (7th Cir. 1996); Soto v. United States, 37 F.3d 252, 255 (7th Cir. 1994); Barker v. United States, 7 F.3d 629, 633 (7th Cir. 1993); United States v. Payton, 260 F.3d 898, 900 (8th Cir. 2001). Here, the trial court repeatedly explained the elements of the charge against Aziz, including the “armed” element, and after acknowledging that he understood, Aziz admitted his guilt. Aziz thus cannot demonstrate that he suffered prejudice as a result of his counsel’s deficient performance. The Appellate Court’s decision was correct and therefore reasonable. See *614Washington v. Smith, 219 F.3d 620, 628 n. 5 (7th Cir. 2000) (“We think it is safe to assume that there is no such thing as a correct, yet unreasonable, application of federal law.”).

AFFIRMED.