
573 F.3d 1124 (2009)
MESA AIR GROUP, INC., a Nevada corporation, Freedom Airlines, Inc., a Nevada corporation, Plaintiffs-Counter Defendants-Appellees,
v.
DELTA AIR LINES, INC., a Delaware corporation, Defendant-Counter Claimant-Appellant.
No. 08-13733.
United States Court of Appeals, Eleventh Circuit.
July 1, 2009.
*1126 David E. Meadows, Dwight J. Davis, Ryan Joseph Szczepanik, W. Ray Persons, Chilton Davis Varner, King & Spalding, Atlanta, GA, for Delta Air Lines, Inc.
G. Lee Garrett, Jr., David M. Monde, Jones & Day, Atlanta, GA, for Plaintiffs.
Before MARCUS, ANDERSON and CUDAHY,[*] Circuit Judges.
CUDAHY, Circuit Judge:
Freedom Airlines has been a regional carrier for Delta Air Lines since 2005. After Delta sought to terminate its regional connection agreement with Mesa Air Group, Freedom's corporate parent,[1] Mesa commenced this action seeking an injunction prohibiting Delta from terminating the agreement. The district court granted Mesa's motion for a preliminary injunction, holding, inter alia, that Mesa had shown a substantial likelihood of success on its equitable estoppel claim. We affirm.


*1127 I. BACKGROUND
The district court's factual findings, which we review for clear error, Fischer v. S/Y NERAIDA, 508 F.3d 586, 592 (11th Cir.2007), were these: in 2005, Mesa and Delta entered into an agreement for Mesa to act as a Delta regional carrier  to operate its own aircraft under the Delta name and to service Delta passengers on Delta-scheduled flights.[2] Initially, Mesa operated out of Orlando, Florida. Subsequently, Delta asked Mesa to operate flights out of New York's John F. Kennedy Airport.
JFK has worse weather and more airspace congestion than Orlando, which makes flight cancellations more common. The increased likelihood of cancelled flights was significant because the Connection Agreement rewards Mesa for months where it achieves a high "completion rate," and authorizes Delta to terminate the contract if Mesa's completion rate falls below 95% for three months of any period of a consecutive six-months.
The Connection Agreement does not define "completion rate." Initially, the parties understood "completion rate" to mean the ratio of scheduled flights to flights that actually reach their destination. However, flights may be cancelled for a number of reasons. They may be cancelled by the FAA based on weather, or by air traffic control based on congestion. Alternatively, they may be cancelled in advance by the carrier itself when the carrier anticipates unfavorable conditions. Specifically, when a carrier anticipates that only a portion of scheduled flights will be allowed to depart, it may of its own initiative cancel lower priority flights to increase the likelihood that higher priority flights will reach their destinations. This is called a "coordinated cancellation."
Between 2005 and 2006, when Mesa was operating out of Orlando, its completion rate was often over 99%. During this period, Mesa counted coordinated cancellations against its reported completion rate, and did not report such cancellations to Delta as a separate statistic.
Because JFK's less hospitable operating conditions had the potential to affect not only Mesa's compensation but also its ability to meet the Connection Agreement's renewal targets, Mesa sought assurances from Delta that Mesa would not be penalized by the move. Mesa was particularly concerned about coordinated cancellations, which were much more common at JFK than at Orlando.[3] In early 2007, Delta's COO assured Mesa's CEO that Delta would work with Mesa to make appropriate modifications to the parties' agreement to ensure that Mesa would not be penalized by the move to JFK. Subsequently, Delta manager Courtney Boyd promised Mesa COO Jorn Bates that coordinated cancellations would not be counted toward Mesa's completion rate. In reliance on these verbal assurances, Mesa subsequently agreed to hundreds of coordinated cancellations. It also stopped counting coordinated cancellations toward its completion rate and billed Delta accordingly. Between September 2007 and January 2008, Delta paid Mesa based on its reported completion rate calculation (which did not count coordinated cancellations) without objection.
The parties' relationship took a turn for the worse in 2008. In March 2008, Delta senior management met to discuss a plan to respond to rising fuel prices by "actively *1128 enforcing exit provisions in contracts" in order to reduce regional jet capacity. The plan singled out the Mesa Connection Agreement for cancellation. Subsequently, Delta initiated negotiations to buy out the Mesa contract, and, when negotiations proved unsuccessful, Delta sent Mesa a letter terminating the Connection Agreement ostensibly based on Mesa's completion rates for October 2007, December 2007 and February 2008. There is no dispute that Mesa's completion rate fell below 95% in February 2008 regardless of the method of accounting for coordinated cancellations. However, if coordinated cancellations are excluded, Mesa's completion rate for October and December of 2007 was well over 95%.[4]
A week after receiving Delta's termination notice, Mesa commenced this action seeking an order enjoining Delta from terminating the Connection Agreement. Mesa subsequently moved for a preliminary injunction, arguing, inter alia, that Delta should be equitably estopped, based on its assurances that it would not do so, from counting coordinated cancellations toward Mesa's completion rate. The district court granted Mesa's motion for a preliminary injunction.

II. DISCUSSION
Our review of a district court's decision granting a preliminary injunction is somewhat complex: we review legal conclusions de novo, Keener v. Convergys Corp., 342 F.3d 1264, 1267 (11th Cir.2003), factual findings for clear error, Fischer, 508 F.3d at 592, and the ultimate decision to grant or deny the injunction for abuse of discretion. BellSouth Telecomms., Inc. v. MCImetro Access Transmission Svcs., LLC, 425 F.3d 964, 968 (11th Cir.2005).
To obtain a preliminary injunction, the moving party must show (1) substantial likelihood of success, (2) irreparable harm, (3) that the balance of equities favors granting the injunction and (4) that the public interest would not be harmed by the injunction. BellSouth, 425 F.3d at 968. Only the first element of this test is at issue here: Delta argues that Mesa has not shown a substantial likelihood of success on its estoppel claim. It argues first that the district court erred by applying New York law to Mesa's estoppel claim, and second that the district court's factual findings were insufficient as a matter of New York law to support estoppel.
As a threshold matter, we hold that the district court correctly applied New York law to Mesa's estoppel claim. The Connection Agreement contains a choice-of-law provision stating that the agreement is subject to New York law. Although Delta argues that this choice-of-law provision does not apply to equitable claims, it conceded at oral argument that it did not make this argument below. Thus, its argument that New York law should not apply to Mesa's estoppel claim is waived. See Daewoo Motor Am., Inc. v. Gen. Motors Corp., 459 F.3d 1249, 1256-57 (11th Cir.2006) (holding that choice-of-law arguments, if not properly presented to the district court, are waived).[5]
*1129 Applying New York law to Mesa's estoppel claim, we agree with the district court that Mesa has shown a substantial likelihood of success. Under New York law, "[a]n estoppel rests upon the word or deed of one party upon which another rightfully relies and so relying changes his position to his injury." Nassau Trust Co. v. Montrose Concrete Prods. Corp., 56 N.Y.2d 175, 451 N.Y.S.2d 663, 436 N.E.2d 1265, 1269 (1982) (internal quotation marks omitted). The elements of estoppel, in other words, are (1) a false representation, (2) reasonable reliance and (3) a detrimental change of position.[6] Delta argues that the district court's factual findings were insufficient to establish any of these elements. We disagree.

A. False representation
Delta argues that there was no evidence that it made false representations to Mesa. Specifically, it argues that the district court's findings establish at most that it failed to correct Mesa's mistaken belief that the parties had reached an agreement not to count coordinated cancellations toward Mesa's completion rate; silence, it claims, does not constitute a false representation as a matter of New York law.
This argument is wide of the mark for two reasons. First, under New York law, words or conduct may give rise to estoppel. Nassau Trust, 451 N.Y.S.2d 663, 436 N.E.2d at 1269. Here, the evidence was that, after Mesa and Delta allegedly agreed to modify the Connection Agreement, Mesa Chief Operating Officer Jorn Bates sent Delta an email memorializing this agreement and Mesa representatives sent multiple followup emails referencing the agreement, to which Delta never responded. The evidence also showed that, knowing that Mesa believed that the parties had agreed that coordinated cancellations would not be counted against it and that Mesa had begun excluding coordinated cancellations from its invoices, Delta paid Mesa's invoices without objection. Even without more, Delta's failure to take reasonable steps to correct Mesa's alleged misunderstanding seems to us sufficient "conduct" to satisfy New York's falsity requirement. See, e.g., John Robert P. v. Vito C., 23 A.D.3d 659, 804 N.Y.S.2d 802, 804 (App. Div.2d Dep't *1130 2005) (noting that false conduct includes "the failure to promptly assert a right [where such failure] has given rise to circumstances rendering it inequitable to permit the exercise of the right").
Further, Delta glosses over the most significant evidence in support of the district court's finding. After Delta assured Mesa that Delta was willing to modify the terms of the Connection Agreement, Mesa COO Jorn Bates testified that he met with Delta manager Courtney Boyd, who assured Bates that coordinated cancellations would not be counted toward Mesa's completion rate. Boyd, of course, denies this. But the district court specifically credited Bates' testimony and found Boyd to be non-credible. In the light of this credibility determination, which Delta does not challenge in its brief,[7] there can be no serious question that there was a sufficient basis for the district court's finding that Delta had made false representations to Mesa.

B. Reasonable reliance
Delta also argues that the district court's finding that Mesa relied on Delta's false representations was clear error. Delta argues that the district court placed too much emphasis on the fact that Delta paid Mesa's invoices claiming credit for coordinated cancellations. According to Delta, Mesa could not have relied on these payments because the payments were made after Mesa already agreed to cancel the flights: the invoices were not paid until 2008, whereas Mesa agreed to cancel the flights in 2007.
Again, this argument simply overlooks Mesa's allegation that Delta orally agreed not to count coordinated cancellations toward Mesa's completion rate. According to Mesa, this agreement took place in late March or early April of 2007. Subsequently, Mesa agreed to cancel more than 400 flights at Delta's request. The evidence that there was such an agreement was clearly enough to support the district court's finding of reliance. That Delta paid Mesa's invoices without objection merely corroborated Mesa's version of events.
Delta's better argument, which it made in oral argument but not in its brief, is that Mesa's reliance was unreasonable under the circumstances because the Connection Agreement's "no oral modifications clause" gave Mesa notice that oral agreements were to have no effect. Delta argues that the purpose of the "no oral modifications" clause is to warn the parties not to rely on side agreements between their representatives, and therefore to give Delta assurance that it would not be bound by allegations concerning the incidental contacts between lower-level representatives. According to Delta, such assurance is particularly important in cases like this, where large companies have an ongoing relationship and contacts take place on a daily basis between the parties' representatives.
*1131 Because Delta did not make this argument in its briefs, we need not consider it here. For the sake of completeness, however, we note that while Delta's argument has some intuitive appeal, Mesa's claim is governed by New York law. See Erie R.R. Co. v. Tompkins, 304 U.S. 64, 78, 58 S.Ct. 817, 82 L.Ed. 1188 (1938) ("Except in matters governed by the Federal Constitution or by Acts of Congress, the law to be applied in any case is the law of the state."). The only question, therefore, is whether under New York law, oral representations can trigger estoppel notwithstanding the existence of a "no oral modifications" clause.
The Nassau Trust case, which is the leading case on New York's law of estoppel, gives an affirmative answer to this question. Nassau Trust involved a foreclosure action under a mortgage agreement that contained a "no oral modifications" provision. 451 N.Y.S.2d 663, 436 N.E.2d at 1267. In spite of the existence of the "no oral modifications" provision, the court held that the plaintiff/mortgagee could be estopped. Indeed, the Court of Appeals reached this conclusion in spite of the fact that the dissent made the same argument that Delta makes here. Id. at 1273 (Jasen, J., dissenting) (arguing that the "no oral modifications provision" is "designed precisely to avoid litigation, such as presented by this case, which is based on mere bare allegations of oral waivers"). This shows that, under New York law, estoppel may be invoked to prevent the exercise of contractual rights, even when that contract contains a "no oral modifications" clause.
The Nassau Trust case also contains a discussion that explains the court's rejection of the argument that the dissent made in that case and that Delta makes here. The court noted that a modification is a more far reaching remedy than an estoppel. Id. at 1269. Because a modification permanently changes an contract's terms, whereas an estoppel requires only a specific act of forbearance, it stands to reason that New York courts would require at least as great a showing of proof to establish the former.[8]


*1132 C. Detrimental Change

Nor, finally, can we agree with Delta that Mesa cannot show that the flights that Mesa agreed to cancel as a courtesy to Delta would have reached their destination but for Delta's actions. The district court found that Mesa had a legal right to refuse to comply with Delta's cancellation requests, and credited Mesa witnesses who testified that they would have immediately stopped acquiescing to Delta's requests if they had known that Delta intended to count hundreds of coordinated cancellations toward Mesa's completion rate. Further, the record suggests that during this period, Delta directed the cancellation of Mesa flights in order to give preference to its own flights. For instance, during October and December of 2007, Delta ordered the cancellation of 5.5% of Mesa's flights. By contrast, Delta cancelled approximately 1.6% of its own flights during this period. In October 2007 alone, Delta directed the cancellation of 78 Mesa flights while cancelling only 8 of its own. In light of all this, it was not clear error for the court to find that but for Delta's assurances, Mesa would likely have operated a number of the flights that were cancelled at Delta's request.

III. CONCLUSION
The evidence showed that Delta induced Mesa to agree to Delta's coordinated cancellations by promising not to count such cancellations against it and then, having benefitted from Mesa's willingness to extend Delta this courtesy, attempted to cancel the parties' contract on the theory that this promise was invalid as a matter of law. In the light of this evidence, the district court did not abuse its discretion when it granted Mesa's motion for a preliminary injunction.[9]
AFFIRMED.
NOTES
[*]  Honorable Richard D. Cudahy, United States Circuit Judge for the Seventh Circuit, sitting by designation.
[1]  In what follows, we will refer to the plaintiffs-appellees collectively as Mesa.
[2]  Following the district court, we will refer to this contract as the Connection Agreement.
[3]  Mesa's worries proved to be prescient. Between September 2007 and March 2008, Delta directed Mesa to cancel more than 400 flights. By contrast, in the two years Mesa operated out of Orlando, Delta directed only 60 coordinated cancellations.
[4]  For instance, in October 2007, Delta directed the coordinated cancellation of 78 Mesa flights, 4.2% of its monthly schedule. If these cancellations were not counted against it, Mesa's completion rate for the month would have been 98.4%.
[5]  Delta's argument that it should be relieved of the consequences of this waiver because it was not given fair notice of Mesa's estoppel claim is without merit. Mesa's memorandum in support of its motion for a preliminary injunction stated that "through its conduct and assurances to Mesa, Delta is also estopped from terminating the Contract ..." (No. 1:08-CV-1334-CC, Doc. no. 24, Ex. 1 at 19-20.) Delta, in turn, responded by arguing that under New York law, Mesa "cannot prevail on [its] claim for equitable estoppel." (Id., Doc. no. 27 at 20.) Thus, Delta had actual notice of Mesa's estoppel claim and was able to respond.
[6]  New York's Appellate Divisions have adopted slightly different formulations of the test for estoppel. On the test that the First Department has adopted, estoppel requires merely lack of knowledge by the party claiming estoppel, rather than an actual false representation by the party to be estopped. See River Seafoods, Inc. v. JPMorgan Chase Bank, 19 A.D.3d 120, 796 N.Y.S.2d 71, 74 (App. Div. 1st Dep't 2005). The Second and Third Departments, by contrast, require a false representation, but do not explicitly require a detrimental change in position. See Benincasa v. Garrubbo, 141 A.D.2d 636, 529 N.Y.S.2d 797, 800 (App. Div.2d Dep't 1988); Hayden v. S & W Meat & Poultry, 221 A.D.2d 823, 634 N.Y.S.2d 226, 227 (App. Div.3d Dep't 1995). Finally, the Fourth Department has adopted a "kitchen sink" approach that incorporates all of the elements of the other Appellate Divisions' tests, requiring (1) a false representation or concealment of material facts, (2) intent to induce reliance, (3) actual reliance, (4) knowledge of the true facts by the party to be estopped, (5) lack of knowledge of the true facts by the party seeking estoppel and (6) a prejudicial change in position. See Airco Alloys Div., Airco Inc. v. Niagara Mohawk Power Corp., 76 A.D.2d 68, 430 N.Y.S.2d 179, 187 (App. Div. 4th Dep't 1980).

These subtleties do not obviously make a great deal of difference. At any rate, because we are bound to apply the law as it has been announced by the New York Court of Appeals, Erie R.R. Co. v. Tompkins, 304 U.S. 64, 78, 58 S.Ct. 817, 82 L.Ed. 1188 (1938), we assume that under New York law, the elements of estoppel are those that were outlined in the Nassau Trust case.
[7]  During oral argument, Delta's counsel argued that this finding was clear error. However, this argument was not made in Delta's opening brief, or indeed its reply brief, and is therefore waived. See Access Now, Inc. v. Southwest Airlines Co., 385 F.3d 1324, 1330 (11th Cir.2004). At any rate, the argument also lacks merit. We owe the district court's credibility determinations a great deal of deference. See CBS Broad., Inc. v. EchoStar Commc'ns Corp., 450 F.3d 505, 517 n. 23 (11th Cir.2006). In the present case, the most probative evidence of the existence of an oral agreement was the witnesses' live testimony. Further, while there was some evidence to corroborate Boyd's version of events  and perhaps a fuller record would show that the facts are as Delta says  there was also a great deal of evidence corroborating Bates' testimony. Thus, the record does not show that the district court's decision to credit Bates' testimony and to discredit Boyd's was clear error.
[8]  During oral argument, Delta relied primarily on Jewell v. Irvmac Shoe Shops, Inc., 19 Misc.2d 815, 187 N.Y.S.2d 412 (Sup.Ct.1959), as authority for the proposition that the "no oral modifications" clause precludes the invocation of equitable estoppel. As a procedural matter, Jewell is of dubious relevance. Again, Mesa's claim is governed by New York law. Typically, we look to decisions from the highest court, here the New York Court of Appeals, to elucidate state law. See Erie, 304 U.S. at 78, 58 S.Ct. 817 (suggesting that "the law of the state shall be declared by its Legislature... or by its highest court..."). When the highest court has not addressed an issue, we may look to intermediate appellate court decisions. See Comm'r v. Estate of Bosch, 387 U.S. 456, 465, 87 S.Ct. 1776, 18 L.Ed.2d 886 (1967) ("[A]n intermediate appellate state court... is a datum for ascertaining state law which is not to be disregarded by a federal court unless it is convinced by other persuasive data that the highest court of the state would decide otherwise.") (internal quotation marks omitted). However, Jewell is a state trial court decision  indeed, it is a fifty year-old decision following a summary proceeding. On no interpretation of Erie of which we are aware is a decision by a state trial court be credited as determining the law of the state.

At any rate, Jewell is inapposite. Jewell involved an action to collect unpaid rent. The tenant alleged that the landlord orally promised to reduce his rent by $150 per month, and claimed that the landlord was estopped from enforcing the lease as written. The court rejected the tenant's argument. However, the decision sheds no light on the present case. The court there did not analyze whether the existence of a "no oral modifications" clause precludes the invocation of equitable estoppel. Instead, the court concluded the equitable estoppel did not apply in that case because the tenant had not shown detrimental reliance. 187 N.Y.S.2d at 415. Thus, even if the Jewell decision could elucidate New York law, the decision, if anything, seems to stand for the rather unsurprising proposition that estoppel cannot be used to frustrate the enforcement of a written instrument where the estoppel claim fails on the merits.
[9]  Having found this, we need not reach Mesa's alternative argument that Delta's attempt to terminate the Connection Agreement breached its implied duty of good faith.
