POSNER, Circuit Judge.

Section 1014 of the federal criminal code provides so far as relevant to this case that "whoever knowingly makes any false statement . . . for the purpose of influencing in any way the action of . . . any bank the deposits of which are insured by the Federal Deposit Insurance Corporation" shall be guilty of a felony. 18 U.S.C. § 1014. Phillip White was convicted of having violated this statute by making knowingly false statements to American Fletcher Leasing Corporation, a wholly owned subsidiary of American Fletcher National Bank, which is a bank whose deposits are insured by the FDIC. The question is whether the subsidiary is also an FDIC-insured bank within the meaning of section 1014. True, the statute does not require that the false statement be made to the insured bank; it is enough that the statement, to whomever made, was intended to influence the bank's action. United States v. Lentz, 524 F.2d 69, 71 (5th Cir. 1975). But the indictment in this case does not charge, and the government does not argue, that White made statements to the leasing corporation intending to influence its parent, the national bank, as in United States v. Maalouf, 514 F. Supp. 851 (E.D.N.Y. 1981). The only entity he sought to influence, so far as the government is concerned, is the leasing corporation. It is therefore crucial to determine whether the leasing corporation is a federally insured bank within the statute's meaning.

The evidence on this question is sparse, but a negative answer seems inevitable. The leasing corporation was incorporated pursuant to Indiana's general corporation law, which at the time the false statements were made expressly prohibited corporations incorporated under it from engaging in the banking business. Ind. Code § 23-1-2-1 (repealed, effective August 1, 1987, by P.L. 149-1986, § 65). This prohibition is repeated in the leasing corporation's articles of incorporation, and there is no suggestion that it was violated. The leasing corporation not only could not lawfully accept deposits; it did not accept deposits. The record is (otherwise) silent on the source of its funds. We know only that the leasing corporation was engaged in equipment financing for the transportation industry and that it did not file a separate financial statement; instead, its assets, liabilities, and earnings were consolidated with those of the parent bank. The government is unable to say whether, should the leasing corporation go broke, its creditors would be able to pierce the corporate veil and reach the bank's assets. The government does point out however that because the Comptroller of the Currency, who regulates national banks, regards the business of the leasing corporation as "incidental to the business of banking," the leasing corporation comes within a regulation of the Comptroller that subjects subsidiaries so engaged to all laws and regulations applicable to national banks. 12 D.F.R. §§ 5.34(c), (d)(2).

At first glance the government's position regarding the bank status of the leasing corporation seems, despite the Comptroller's regulation, utterly untenable. The statute is clear. It punishes the making of a false statement for the purpose of influencing a bank that has federally insured deposits. White made his false statements to, and for the purpose of influencing, a corporation that is not a bank, that does not have federally insured deposits — that does not have deposits, period.

At second glance the government's position still seems untenable. Here we go behind the language of the statute to its purpose. The statute forbids the making of false statements intended to influence any of a host of federal financial institutions, plus institutions such as federally insured banks and savings and loan institutions in which the federal government has a financial stake as insurer or backer. So far as appears, the federal government has no stake in the fortunes of the American Fletcher Leasing Corporation. The primary and sole relevant purpose of requiring a bank to conduct its nonbanking business through subsidiaries is to insulate the depositors, and hence their federal insurer, the FDIC, from liabilities that may be incurred as a result of ventures riskier than banking itself. Of course a parent is not always able to insulate itself fully. If it makes representations to the subsidiary's creditors that it stands behind the subsidiary's debts, and the subsidiary becomes insolvent, a court may pierce the corporate veil and allow the creditors to reach the parent's assets; or the court may hold the parent directly liable on a theory of estoppel. Or, again if the subsidiary becomes insolvent, the parent may consider it on balance good business to pay its subsidiary's debts rather than incur the ill will of the subsidiary's creditors. Even more likely is financial assistance from the parent designed to prevent the subsidiary from becoming insolvent in the first place, an event that might impair the parent's commercial standing. See generally Black, Miller Posner, An Approach to the Regulation of Bank Holding Companies, 51 J.Bus. 379, 392-99 (1978).

All this is just to say, however, that the economic fortunes of a corporation and its affiliates are intertwined; and this is so whatever the character of the subsidiary's business. The subsidiary might be a travel agency, or an insurance agency — these are common examples of enterprises affiliated with banks. Yet the government — by which we mean the office of the United States Attorney in Indianapolis, for we were told at argument that the office did not attempt to clear its position on the scope of section 1014 with the U.S. Attorney's superiors in the Department of Justice — does not press its argument this hard. It does not contend, for example, that someone who holds up a travel agency that happens to be owned by a federally insured bank is guilty of bank robbery in violation of 18 U.S.C. § 2113(f), a statute that protects the same banks as section 1014. The government clings to the regulation subjecting a national bank's subsidiaries to all banking laws and regulations — as if the Comptroller of the Currency had the authority to expand the scope of a federal criminal statute — and by doing so incidentally drives a wedge between national banks and all other federally insured banks, a distinction nowhere reflected in section 1014. In fact the government at oral argument was completely unwilling to delimit the scope of section 1014 with regard to subsidiaries. It said that no sharp line can be drawn — the line will have to be pricked out by a process of case-by-case decision.

We are not deeply troubled by the fact that, had Mr. White read Title 18 before deciding to make false statements designed to influence American Fletcher Leasing Corporation, he probably would not have thought he was running a risk of being punished under section 1014. Doctrines of vagueness in criminal and constitutional law are designed more to limit the discretion of police and prosecutors than to ensure that statutes be intelligible to lay persons pondering criminal activity. See United States v. Gardner, 860 F.2d 1391, 1394 (7th Cir. 1988); Waldron v. McAtee, 723 F.2d 1348, 1354 (7th Cir. 1983) (citing Supreme Court cases). This is clear from cases such as Rose v. Locke, 423 U.S. 48, 96 S.Ct. 243, 46 L.Ed.2d 185 (1975) (per curiam), which hold that the requisite fair notice can be provided by judicial decisions construing a vague statute, though few criminals are careful readers of judicial reports until they are imprisoned and have leisure to explore the prison's law library. Provided that conduct is of a sort widely known among the lay public to be criminal — and efforts to obtain money by false pretenses are in that category — a person is not entitled to clear notice that the conduct violates a particular criminal statute. It is enough that he knows that what he is about to do is probably or certainly criminal. See, e.g., United States v. Feola, 420 U.S. 671, 678, 95 S.Ct. 1255, 1261, 43 L.Ed.2d 541 (1975); Knustson v. Brewer, 619 F.2d 747, 750 (8th Cir. 1980). Thus it is a federal crime to assault a federal officer whether or not the assailant has any reason to believe that his victim is a federal officer. United States v. Feola, supra, 420 U.S. at 684-86, 95 S.Ct. at 1263-65.

Feola, it is true, was a case in which the ambiguity lay in the circumstances in which the statute was applied rather than in the statute itself; but the principle is the same. It is therefore merely a detail that no one reading section 1014 could be expected to tumble to the fact that making false statements to, and for the purpose of influencing, a corporation that was not a bank and that was forbidden by statute and by its own articles of incorporation to engage in the banking business — a corporation that did not have deposits, let alone federally insured deposits — was nevertheless a bank whose deposits are insured by the FDIC. And it is likewise a detail that such a person would have no way of dispelling any doubt he felt, because even the government is unable to say which bank subsidiaries are covered by 1014. All the Indianapolis U.S. Attorney's office knows for sure is that the subsidiary in this case is within that scope — but why it thinks this eludes us, for it does not argue that there is a federal interest in preventing frauds against equipment-leasing subsidiaries of federally insured banks. Such looseness of interpretation creates a potential problem, given that as we said earlier the primary purpose of the requirement of fair notice of criminal liability is to curb discretion in law enforcement. But it is not a problem here, since White makes no argument based on lack of notice.

What is important here is that the government's interpretation of section 1014 has no support in the language or purpose of the statute, in its sparse legislative history, in case law, in any contention that either the states generally or Indiana in particular lack adequate incentives, or are otherwise reluctant, to prosecute persons who defraud subsidiaries of federally insured banks, or in any other source of potential guidance to statutory interpretation. Section 1014 was amended on December 31, 1970, to add federally insured banks to the list of protected institutions. See generally United States v. Sabatino, 485 F.2d 540, 543-44 (2d Cir. 1973). This was the same day the Bank Holding Act, 12 U.S.C. § 1841 et seq., was amended by an unrelated Act of Congress to allow banks to engage in collateral businesses through affiliated corporations. It would be perilous to assume that by referring, in the amendments to section 1014, to federally insured banks, Congress deliberately excluded their nonbanking affiliates. But it would be even more perilous to assume that Congress wanted to extend the statute's protection to those affiliates, when so far as appears there is no (or only the most attenuated) federal stake in preventing fraud against affiliates of a federally insured bank, as distinct from fraud against the bank itself.

The cases cited by the U.S. Attorney interpret other criminal statutes, worded differently from section 1014. United States v. Fulton, 640 F.2d 1104 (9th Cir. 1981), upheld a conviction for aiding and abetting an embezzlement of funds of a federally insured bank, in violation of 18 U.S.C. § 656. The employee whose embezzlement the defendant aided and abetted was an employee of a bank subsidiary, not of the bank itself. But in the government's own words from its brief in the present case, "the employee's position with the subsidiary mortgage company gave her access to bank funds that were managed by the subsidiary mortgage company" (emphasis added). The funds were the bank's, so the statute was satisfied. Moreover, section 656 requires only that the offender be "connected in any capacity with any . . . insured bank," and the subsidiary's employee could be and was connected with the parent. White is not accused of taking any funds belonging to the American Fletcher National Bank, nor had he any contractual relationship, direct or indirect, with the bank.

United States v. Prater, 805 F.2d 1441, 1446 (11th Cir. 1986), is similar to Fulton except that it arose under section 657 of the Criminal Code, a parallel statute to section 656 which differs only in that it protects institutions insured by the Federal Savings and Loan Insurance Corporation rather than by the FDIC. United States v. Cartwright, 632 F.2d 1290 (5th Cir. 1980), also involved section 657, but there the issue was whether the assets of a wholly owned subsidiary could be said to "belong to" (key words in section 657) the parent bank. The court held they could. Id. at 1292. A wholly owned subsidiary is, by definition, wholly owned by its parent, so it is natural to attribute its assets to the parent. But the direction cannot be reversed. Deposits of the parent are not deposits of the subsidiary.

Interpreting still another piece in the mosaic of criminal statutes designed for the protection of financial institutions, Cartwright holds that the business dealings of a subsidiary are "within the jurisdiction of" the agency that regulates the subsidiary's parent bank. Id. at 1292-93. If this were the test under section 1014, the U.S. Attorney could do much with the regulation it cites that subjects certain subsidiaries of national banks (including the American Fletcher Leasing Corporation) to the Comptroller's regulatory authority. But it is not the test under section 1014.

We repeat that if White had intended by making false statements to the leasing corporation to influence the bank as well, the fact that the statements were not made to the bank would not prevent his conviction; the language of the statute is clear on this point. Nor would the intent to influence the bank have to be the primary motivation for the making of the statements. See United States v. Krown, 675 F.2d 46, 50 (2d Cir. 1982). It would be enough if White had known that the loan he was getting from the leasing corporation would be assigned to the bank. United States v. Bowman, 783 F.2d 1192, 1199 (5th Cir. 1986). But the government proposed no such theory of liability in this case. It was content to show that White made false statements to influence the leasing corporation. It staked its all on persuading the district court and us that the leasing corporation is a bank.

The judgment is reversed with directions to acquit White.