Before WILLETT, ENGELHARDT, and WILSON, Circuit Judges. DON R. WILLETT, Circuit Judge: In 2016, a Texas jury convicted Kirk Engle of felony aggravated assault with a deadly weapon. Engle initiated this postconviction proceeding in federal district court after unsuccessfully petitioning Texas state courts for a writ of habeas corpus. The district court rejected all of Engle’s claims of trial error. Engle then sought a certificate of appealability, which this court granted as to the claim of prosecutorial misconduct. We now consider that claim on the merits. Although we agree with Engle that certain conduct by the prosecutor during the trial violated the Due Process Clause, we conclude that Engle was not prejudiced by the violation. We therefore AFFIRM the judgment below denying habeas relief. I According to trial testimony, the events that gave rise to Engle’s conviction occurred on the evening of August 19, 2014 in Yorktown, Texas. Firefighters from the Yorktown Volunteer Fire Department were called to the scene of a brush fire. When they arrived, Engle was standing nearby and told them he had started the fire intentionally. He taunted the firefighters, saying “f*** the fire department” and discouraging them from putting out the fire. As firefighter Brian Smolik prepared to extinguish the blaze anyway, Engle said, “Do you want to die tonight?” and then stabbed Smolik in the stomach with a knife. When Smolik’s fellow volunteer Monte Riedel moved to intervene, Engle threatened, “Do you want to get stabbed tonight, too?” before fleeing on foot. Eric Von Helbing, another firefighter on the scene, called the police and paramedics. Smolik was transported to the hospital, where he remained for four days, three of which he spent in the ICU. Police quickly found Engle wandering the streets and placed him under arrest. Upon being handcuffed, Engle told the officers, “I was waiting for you,” explaining that he “wanted to go back home” and that “the penitentiary [wa]s [his] home.” The officers discovered through a pat-down of Engle that he had disposed of the knife. Despite thoroughly searching the area, police never recovered the weapon. As the officers were transporting Engle to booking, he explained to them that Smolik was “in the wrong place at the wrong time.” Engle further expressed that he found it “hard making it outside of prison” and “didn’t want to get out.” At one point during the ride, Engle overheard one of the officers misspell Engle’s name to dispatch and spoke up to correct the error. Shortly after Engle arrived at the DeWitt County Sheriff’s Office, Texas Ranger Troy Wilson attempted to question Engle about the stabbing. Ranger Wilson entered the interview room, activated his digital audio recorder, and introduced himself to Engle. Engle responded by expressing that he wanted to go back to prison and that “this [was] what it took.” Wilson then gave Engle the Miranda warnings, followed by the warning required by state statute of his right to terminate police questioning.[1] Engle then responded, “terminate” before standing up and being escorted out of the room. A DeWitt County grand jury indicted Engle for felony aggravated assault with a deadly weapon.[2] Engle pleaded not guilty and the case proceeded to a jury trial. Engle did not dispute that he stabbed Smolik. Instead, Engle raised a defense of temporary insanity due to involuntary intoxication. Taking the stand in his own defense, Engle testified that an adverse reaction to the common antidepressant Lexapro caused him to suffer blackouts and fits of rage. Engle admitted on cross examination, however, that he had a longstanding tendency to fly into violent rages even years before he began taking Lexapro, and that he was telling acquaintances in the months leading up to the stabbing that he wanted to return to prison. Importantly for present purposes, the prosecutor also cross-examined Engle regarding his actions when Ranger Wilson attempted to question Engle about the stabbing incident, leading to the following exchange: Q. So — and then [Ranger Wilson] started reading you your rights. Do you remember that? A. I heard it. Q. And he said you have the right to terminate the interview at any time, didn’t he? A. Yes, sir. Q. And what did you say? A. Terminate. Q. You said terminate. Stood up and walked out. Sounds like you knew exactly what was going on then, doesn’t it? A. It would have made more sense if I tried to tell him my side of the story. Q. Would it make more sense in what way? What do you mean? A. Like right now, if I talked to him I’ll tell him my side. Q. Uh-huh. A. At that time I was not in my right mind. I was talking but I was not in my right mind. Q. But, for whatever reason, he reads you your rights, he gives you one of them, which is that you’ve got the right to terminate this at any time, and you said terminate, stood up and walked out. Right? A. Yes, sir. Q. It sounds as if you knew exactly what he was telling you in your warnings and you understood them and you chose to exercise one of your rights, doesn’t it? A. That’s what it sounds like, sir. In support of his defense, Engle offered testimony from a psychiatrist, Dr. Thomas Demoor, who testified that selective serotonin reuptake inhibitors (SSRIs) such as Lexapro can cause mania, characterized by “increasing agitation or irritability or aggression,” in patients with bipolar depression—a condition from which, “in [Demoor's] opinion,” Engle suffered. Demoor believed that Engle’s adverse reaction to Lexapro “led to a manic state that caused his aggressive outburst.” Demoor admitted, however, that he “couldn’t evaluate [Engle's] state of mind at the time of the event . . . [b]ecause [Engle] told [him] he didn’t remember the event.” Instead, Demoor formed his opinion based on a “review[] [of] [Engle's] medical records,” “the witness statements from the assault,” and “[the State's expert witness] Dr. Kutnick’s reports.” The defense also offered the testimony of three other witnesses. One was a nurse at the DeWitt County Jail who was tasked with administering inmates’ medications. She testified only that Engle began refusing to take Lexapro when he arrived at the facility on the weekend of August 23, 2014, though the prosecutor stressed on cross-examination that this was five days after Engle was arrested for stabbing Smolik. The defense also called a corporal at the same jail who also helped dispense medications to inmates. She testified that shortly after Engle was housed at the jail in connection with the stabbing, he had become “agitated” on occasion after taking Lexapro, “pacing in the cell and yelling and talking loud” before wearing himself out. The corporal admitted on cross-examination that Engle did not harm himself or otherwise act violently during these periods. Engle’s mother also testified on his behalf that she noticed him becoming more “forgetful” and “angry,” and “crying” more often, after starting Lexapro. She admitted on cross- examination that she nonetheless continued to bring the medication to the jail for Engle to use even after his arrest, and that some of his hostile behavior persisted even when he was off Lexapro. The State’s case was naturally aimed at rebutting Engle’s defense of insanity due to involuntary intoxication. The prosecutor elicited testimony about the events surrounding the stabbing and Engle’s subsequent arrest, including Engle’s taunting of the firefighters, his admission to the police that he had been “waiting” for them, and his expressed desire to return to prison. During the prosecutor’s direct examination of Ranger Wilson, Wilson was asked about his questioning of Engle after the arrest, resulting in the following exchange: A I didn’t ask [Engle] any questions at that time, I needed to read him his Miranda rights and other things, that was before, and so did a little housekeeping, read him his Miranda. He said he understood it and as soon as I finished reading his Miranda warnings, the 38.22 warnings, he terminated the interview and walked out. Q. Terminated the interview? A. Yes. Q. How did he terminate it? A. I said, “you have the right to terminate the interview at any time.” He said “terminate,” stood up and walked out. After some further back-and-forth, a recording of the interview was then played for the jury, and the prosecutor then asked, Q. So as you’re going through these warnings that we just heard, what’s the defendant doing, if anything, when you’re asking do you understand that? A. He’s nodding in the affirmative that he understood that right. Q. Show us what you mean. A. Nodding his head up and down. Q. Okay. And at the end when you said he can terminate this interview at any time, what did he say? A. Terminate. Q. Terminate? And then what did he do? A. Stand up and start walking towards the door. The State also brought forth its own expert witness, psychiatrist Dr. Joel Kutnick, who testified that Lexapro was not known to cause rage attacks or temporary “blackouts” of the kind complained of by Engle, and that Engle’s prescribed dose of Lexapro at the time was “a standard dosage.” Kutnick also reviewed multiple reports from mental health professionals who treated or evaluated Engle in the period leading up to the stabbing. Kutnick testified, based on the contents of the reports (which were also admitted into evidence as exhibits), that Engle had never complained to his prescribing doctor about Lexapro’s effects in the past (and had at one point even asked for a higher dose), and that Engle had stated during an evaluation conducted before he began taking Lexapro that he used “rage stages” “as an excuse to become violent.” Kutnick conceded that SSRIs such Lexapro can cause mania in patients with bipolar disorder. Nevertheless, after reviewing the hour-long police footage of Engle’s arrest and subsequent transport to booking so as to observe his demeanor as these events unfolded, Kutnick testified that, in his professional judgment, Engle was not in a manic state at the time. Furthermore, Kutnick explained, Engle was also taking Seroquel (a mood stabilizer) during the period in question, and it was “much more rare” for SSRIs to cause mania even in patients suffering from bipolar depression if they are also taking a mood stabilizer. The State also called a caseworker from the mental health facility that had overseen Engle’s treatment in the roughly four-month period leading up to his attack on Smolik. Throughout that time, Engle was on Lexapro as part of his course of treatment. The caseworker testified that he spent an hour each week with Engle at his home—mainly “to remind him to take medication and reorder prescriptions on time, keep doctors’ appointments” and meet with his parole officer—but that Engle never once reported any complaints about his medication. The prosecutor chronicled all of this evidence of Engle’s sanity in his lengthy summation, during which he also made this comment: Well, [Ranger Wilson] says [to Engle], “okay, well, let me give you your rights and let’s see, you know, let’s talk about it some more,” and he goes, “you have the right to terminate your interview.” What does [Engle] say? He says “terminate,” stands up and walks out. Now, that doesn’t sound like an insane person to me. The jury found Engle guilty of the charged offense of felony aggravated assault with a deadly weapon. The trial judge then found that Engle was a habitual offender under TEX. PENAL CODE § 12.42 and accordingly sentenced him to forty years’ incarceration. His conviction was affirmed on direct appeal, with the appellate court rejecting Engle’s sole point of error regarding the limitations on his expert witness’s testimony.[3] In September 2017, Engle filed a petition for a writ of habeas corpus in Texas state court, raising several claims of error, including prosecutorial misconduct. The Texas Court of Criminal Appeals denied his petition without a written opinion. Engle then initiated this postconviction proceeding in federal district court, seeking habeas relief under 28 U.S.C. § 2254. The district court rejected all five of Engle’s grounds for relief.[4] Engle then moved this court for a certificate of appealability (COA),[5] which was denied as to all his claims except: whether the prosecution engaged in misconduct by commenting on Engle’s post-arrest, post-Miranda silence to rebut his defense of insanity by involuntary intoxication, Doyle v. Ohio, 426 U.S. 610 (1976); Wainwright v. Greenfield, 474 U.S. 284 (1986), and, if so, whether this misconduct had a “substantial and injurious effect or influence in determining the jury’s verdict.” United States v. Chavez, 193 F.3d 375, 379 (5th Cir. 1999). These are the only issues before us in this appeal. II Our review of collateral attacks on state criminal convictions is governed by the federal Antiterrorism and Effective Death Penalty Act (AEDPA). AEDPA states, in relevant part, that a federal court cannot grant a state prisoner’s habeas petition “with respect to any claim that was adjudicated on the merits in State court proceedings”—as both parties agree Engle’s claim was—unless the state court’s decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.”[6] This provision establishes a “‘highly deferential standard for evaluating state-court rulings’” that requires federal courts to give those rulings “the benefit of the doubt.”[7] We cannot conduct “our own independent inquiry into whether the state court was correct as a de novo matter. . . . Relief is available under [AEDPA] only if the state court’s decision is objectively unreasonable.”[8] The question is whether “fairminded jurists could disagree” as to how the Supreme Court’s caselaw applies to the circumstances that the state court confronted; if so, then we cannot set aside the state court’s conclusion.[9] This deference applies even where, as here, the state court has denied habeas relief without a written opinion. In such cases, the habeas petitioner must “show[] there was no reasonable basis for the state court to deny relief.”[10] At the same time, however, “AEDPA does not ‘require state . . . courts to wait for some nearly identical factual pattern before a legal rule must be applied.’”[11] On the contrary, a state court’s application of a principle established by Supreme Court caselaw may still be “unreasonable” for AEDPA purposes even if the state court confronted “a set of facts ‘different from those of the case in which the principle was announced.’”[12] “Certain principles are fundamental enough that when new factual permutations arise, the necessity to apply the earlier rule will be beyond doubt.”[13] * * * With these principles in mind, we consider Engle’s claim of prosecutorial misconduct. During his trial, the prosecutor elicited testimony that Engle had invoked his right to terminate police interrogation after being advised of this right. The prosecutor then argued to the jury during his summation that Engle’s termination of the interview was evidence that Engle was sane at the time of the offense. Engle argues that the prosecutor’s conduct in doing so deprived Engle of “due process of law” in violation of the Fourteenth Amendment.[14] Moreover, Engle contends, the Supreme Court’s caselaw clearly establishes that the prosecutor’s actions violated the Due Process Clause. We agree with Engle on both points. In Doyle v. Ohio, the Supreme Court held that the “use for impeachment purposes” of a criminal defendant’s “silence, at the time of arrest and after receiving Miranda warnings, violate[s] the Due Process Clause.”[15] The Court reasoned that, although “the Miranda warnings contain no express assurance that silence will carry no penalty, such assurance is implicit to any person who receives the warnings,” and hence “it would be fundamentally unfair” to allow that person’s “silence to be used to impeach an explanation subsequently offered at trial.”[16] It made no difference that the defendants in that case, “when cross-examined about their silence, did not offer reliance on Miranda warnings as a justification. . . . After an arrested person is formally advised” that “he has a right to remain silent, the unfairness occurs when the prosecution undertake[s] impeachment on the basis of what may be the exercise of that right.”[17] The Court relied on Doyle a decade later in Wainwright v. Greenfield, which held that the Due Process Clause also prohibits a prosecutor from rebutting an insanity defense by using a defendant’s “silence after receiving Miranda warnings []as evidence of his sanity.”[18] Moreover, the Court explained, “silence” in this context “does not mean only muteness; it includes the statement of a desire to remain silent, as well as of a desire to remain silent until an attorney has been consulted.”[19] On the other hand, the Supreme Court has declined to apply Doyle in cases where defendants had not been Mirandized, reasoning that, “[i]n the absence of the sort of affirmative assurances embodied in the Miranda warnings,” it does not “violate[] due process of law for a State to permit cross-examination as to postarrest silence when a defendant chooses to take the stand.”[20] The key difference between such cases and those in which the Court found a due-process violation was that the latter involved government action that frustrated defendants’ reliance on official assurances of their rights.[21] We think it follows naturally and necessarily from this caselaw that the prosecution in this case violated Engle’s due-process rights. At the outset of custodial interrogation following his arrest, Ranger Wilson gave Engle the statutorily required warning that he “ha[d] the right to terminate the interview at any time.” Engle immediately invoked this right. The prosecutor subsequently relied on that invocation at trial as evidence of Engle’s sanity. Just as in the cases discussed earlier in which the Supreme Court found a due- process violation, the State advised Engle of his rights and thereby “implicitly promise[d] that any exercise of those rights w[ould] not be penalized,” but “then s[ought] to make use of [his] exercise of those rights in obtaining his conviction.”[22] The State, in doing so, violated the clearly established strictures of the Due Process Clause, as construed by the Court. The State argues, however, that Doyle and Wainwright are different from this case in an important respect: the defendants in the former two cases invoked their right to silence in reliance (or at least presumed reliance) on the warnings required by Miranda, whereas Engle invoked his right to terminate police questioning in reliance on a warning required by Article 38.22 of the Texas Code of Criminal Procedure.[23] The State correctly points out that, although Miranda established a right to terminate custodial questioning, this was not one of the rights of which the Court held that suspects must be apprised before questioning begins.[24] Thus, in the State’s view, the Supreme Court has not spoken to the question at hand—that is, whether a defendant’s reliance on warnings required by mere state statute should be treated the same as a defendant’s reliance on warnings required by the Miranda decision. We do not believe that the State’s proffered distinction between this case and the applicable Supreme-Court precedent is material. Doyle and the Court’s subsequent cases applying its holding, as we read them, establish that a due-process violation occurs whenever (1) a defendant is assured by the authorities that he has a certain right, (2) the defendant exercises the right, and (3) the prosecution uses the defendant’s exercise of the right as evidence against him at trial. It makes no difference whether the assurance given to the defendant was required by the federal Constitution or instead by statute, as in this case; it is the defendant’s frustrated reliance on an official assurance that violates the Constitution. The warning required by Article 38.22 of the Texas Code of Criminal Procedure of a suspect’s right to terminate interrogation, no less than the warnings required by Miranda, carries with it the “implicit [assurance] to any person who receives the warning[]” that invoking the right to terminate “ will carry no penalty,” and hence it would be just as “fundamentally unfair . . . to allow” such an invocation to be used against a defendant at trial as it would to do the same with a defendant’s Miranda-induced choice to remain silent.[25] “The implicit promise, the breach, and the consequent penalty are identical in both situations.”[26] Indeed, the Court’s reasoning in Doyle confirms that the source of the right on whose assurance a defendant relies is irrelevant. The Doyle majority supported its holding by citing a prior case where the Court had held that it was improper for a prosecutor to ask jurors to draw adverse inferences from a defendant’s refusal to answer a question at trial that the judge (incorrectly) told the defendant he had the right not to answer.[27] “[B]ecause the privilege had been granted, even if erroneously,” the Doyle Court explained, “the requirements of fair trial made it error for the trial court to permit comment upon the defendant’s silence.”[28] Obviously, then, Doyle‘s due-process holding is not confined to instances in which defendants have detrimentally relied on assurances of their rights under the federal Constitution, since Doyle favorably cited a case in which a defendant had detrimentally relied on an assurance that was not required by any provision of law. And if it violated the Due Process Clause to frustrate a defendant’s reliance on an incorrect assurance that he had a right not to answer a particular question, then surely it violated the Due Process Clause to frustrate Engle’s reliance on a correct assurance that he had the right to terminate police questioning. Our confidence in our understanding of the Supreme Court’s decisions is fortified by caselaw from other courts that reflects a similar understanding.[29] For instance, the Texas Court of Criminal Appeals has relied on Doyle to hold that a defendant’s invocation of the right to an attorney after being advised of that right could not be offered as evidence against him at trial, even though the advisement was given prematurely (that is, before the right of which the defendant was advised had attached): [A]dverse use of evidence that a defendant invoked a right or privilege which has been granted him, is constitutionally impermissible. This is true even though the right or privilege was erroneously extended to a defendant, because the requirements of a fair trial make it impermissible to tell a defendant that he has a right, even if erroneously, and then use his exercise of that right against him.[30] The high courts of Kentucky and Vermont have also cited Doyle in reaching the same conclusion on similar facts.[31] Collectively, these cases stand for the proposition that Doyle‘s due-process holding is not limited to defendants’ detrimental reliance on assurances required by the U.S. Constitution or Miranda, but rather extends to similar assurances grounded in other sources of law (and even to assurances given by mistake). Most on-point of all, however, is a 1993 decision of the California Court of Appeals in which a criminal defendant had been assured by the authorities that he enjoyed certain statutory rights, yet the prosecutor later introduced the defendant’s exercise of those rights as evidence against him. The court held that the prosecutor’s action violated the Due Process Clause, rejecting an argument reminiscent of the one made by the State in this case: [The state] note[s] that while the rights at the center of Doyle are constitutionally-based, the rights accorded defendant here are statutory creations. . . . [T]his is a distinction without a difference because the principle of unfairness is the same . . . whether the rights at issue are statutorily-created or constitutionally-based . . . . What implicates due process here is not the derivation of the legal rights at issue—constitutional or statutory—but rather the principle that the state cannot provide a right, implicitly assure that its exercise carries no penalty, and then use that exercise as prosecution evidence.[32] To the same effect is a Connecticut court’s decision holding that warnings required by state statute may induce the type of reliance that triggers Doyle.[33] We are persuaded by this reasoning, as well as by that of other courts that have likewise found Doyle-style due process violations where defendants detrimentally relied on assurances of their rights or privileges, even though such rights or privileges were non-constitutional in nature.[34] The parties have not cited, nor have we identified, any cases reaching the opposite conclusion. We submit that “fairminded jurists” could reasonably reach only one conclusion as to how the Supreme Court’s caselaw applies to the facts before us: the prosecutor violated the Due Process Clause when he used Engle’s invocation of his right to terminate custodial interrogation as evidence of sanity, since Engle ostensibly invoked that right in reliance on an official assurance that he was entitled to terminate questioning at any time. III That Engle’s due-process rights were violated does not necessarily mean, however, that he is entitled to habeas relief. He must also demonstrate prejudice—that is, that the constitutional error was sufficiently serious as to call the outcome of his trial into doubt.[35] This is where Engle falls short. In considering Doyle claims raised on collateral attack, federal courts apply the test of prejudice established by the Supreme Court in Brecht v. Abrahamson, which calls on us to “review[] the record to determine whether the alleged error had substantial and injurious effect or influence in determining the jury’s verdict.”[36] Under this standard, “a constitutional trial error is not so harmful as to entitle a defendant to habeas relief unless” he shows that “there is more than a mere reasonable possibility that it contributed to the verdict. It must have had a substantial . . . influence in determining the verdict.”[37] “The Brecht standard applies even when, as here, the state court did not analyze the issue.”[38] We begin our prejudice inquiry by noting that Engle raised the “affirmative defense to prosecution” recognized by Texas law “that, at the time of the alleged offense, the defendant, as a result of a severe mental defect caused by involuntary intoxication, did not know that his conduct was wrong.”[39] “‘[W]rong’ in this context means ‘illegal.’”[40] The defendant bears the burden of proving insanity due to involuntary intoxication by a preponderance of the evidence.[41] Engle does not dispute that the jury charge in his case accurately explained the elements of this defense. Our careful review of the record leaves us with the firm impression that the constitutional violation did not have a substantial effect on the verdict.[42] For one, the prosecution’s references to Engle’s termination of questioning were relatively infrequent.[43] That fact was mentioned in the prosecutor’s opening argument and again during his direct examination of Ranger Wilson, but only twice did the prosecutor suggest any kind of connection between Engle’s termination of questioning and his sanity: during an exchange with Engle on cross-examination (which comprised less than two pages of an approximately 70-page transcript of Engle’s cross-examination and a nearly 300-page guilt-phase trial transcript), and once more during the prosecutor’s roughly 6,100-word summation, of which less than 60 words (about four sentences) made any reference to Engle’s termination of questioning. Moreover, the prosecutor’s fleeting mentions of Engle’s invocation of his right to terminate police questioning were merely cumulative of the State’s other, far stronger evidence of Engle’s lucidity at the time he stabbed Smolik.[44] The prosecution elicited testimony that, just before the assault, Engle explained to the firefighters that he had started the fire on purpose, as well as that Engle told the police who arrested him that he had been “waiting for [them]” and had wanted to return to prison. Engle apparently had the presence of mind at the time of his arrest that, upon overhearing one of the officers misspelling Engle’s name to dispatch, he interjected to correct the spelling. Engle then explained to Ranger Wilson after arriving at the Sheriff’s Office that he wanted to go back to prison and that “ this [was] what it took.” Once the jury had heard the foregoing evidence of Engle’s lucidity at the time of the offense, it is quite implausible that testimony that Engle terminated police interrogation by uttering a single word—a fact far less probative of his sanity than the extensive testimony about his contemporaneous interactions with police and firefighters[45]—could have substantially affected the verdict. On the whole, even setting aside the improper mentions of Engle’s invocation of his right to terminate police interrogation, the evidence offered by the State to rebut his claim of temporary insanity was overwhelming.[46] First, there was the testimony recounted earlier regarding his interactions with firefighters and police on the night he was arrested, which indicated that Engle was alert and coherent around the time of the offense. Similarly, the State introduced substantial evidence that Engle had planned the stabbing in advance in order to get himself sent back to prison. That Engle planned his crime beforehand is probative of sanity,[47] and his understanding that stabbing someone would land him in prison reflects Engle’s appreciation of the wrongfulness—that is, illegality—of such conduct. There was also considerable testimony tending to show that Engle’s claims of having been rendered insane by Lexapro were spurious. The State’s expert Dr. Kutnick testified that rage attacks or “blackouts” of the kind Engle claimed to have suffered were not common side effects of Lexapro and were especially unlikely given that he was simultaneously taking a mood stabilizer. Kutnick also testified as to his professional opinion, based on the video evidence and Engle’s mental-health records, that Engle was not experiencing mania or any other form of temporary insanity when he committed the assault. Those records, which were admitted into evidence as exhibits, gave no indication that Engle had ever complained to prescribers about Lexapro’s effects in the past, and indeed indicated that he had once asked for a higher dose. Engle’s mental health caseworker during the months preceding the assault likewise testified that Engle had never mentioned any adverse effects from Lexapro. Finally, there was a wealth of testimony and documentary evidence that Engle had a history of aggressive and violent behavior that began long before he began taking Lexapro. The prosecutor recapped all this evidence in his summation. The evidence Engle offered in support of his insanity defense, on the other hand, was comparatively far weaker and, more importantly, would not have been any stronger if the prosecution had merely omitted mention of his termination of the interview with Ranger Wilson—a fact that was, as was previously explained, cumulative of the State’s other, far stronger evidence of Engle’s lucidity at the time he committed the offense. In light of the other evidence that Engle was not so intoxicated that he could not appreciate the wrongfulness of his conduct, it is virtually inconceivable that the jury would have bought Engle’s defense and acquitted him if the prosecutor had merely omitted mention of the fact that Engle exercised his right to terminate police questioning. Engle has thus failed to raise “grave doubt as to the harmlessness” of the due-process violation at his trial, and accordingly he is not entitled to habeas relief.[48] IV For the reasons explained above, the district court’s judgment denying a writ of habeas corpus is AFFIRMED.