EASTERBROOK, Circuit Judge.

South Water Market and Local 703 of the Teamsters Union had a collective bargaining agreement that ran from 2004 through April 30, 2007. From April to September 2007 they negotiated to reach a new deal. On September 12, 2007, they shook hands on an agreement. Michael Abramson, South Water Market's bargaining representative, was supposed to write up the agreed terms and send them to the Union.

Nothing happened. Howard Murdoch, the Union's president, began sending Abramson emails asking for the text. Abramson promised to provide one but didn't. By February 2008 Murdoch was worried that the pension and welfare funds covering South Water Market's employees represented by the Teamsters would cutoff participation (since the only written contract had expired) or sue. On March 21, 2008, Abramson begged off, stating: "I'm having trouble with my notes."

On April 3 Murdoch sent Abramson a document with the terms that Murdoch's notes said had been agreed. Abramson did not reply, one way or the other — but South Water Market did begin paying the wages, and making the pension and welfare contributions, specified in Murdoch's text. Murdoch also sent the document to the pension and welfare funds, telling them that South Water Market had agreed to its terms. The funds (all of them multi-employer plans) submitted bills calculated according to those terms. South Water Market paid them — until August 2009.

At the end of July 2009 Juventino Castillo retired. He had been one of two workers in the "Warehouse/Driver" classification; he received higher wages, and larger fringe-benefit contributions, than workers in the "Grocery Workers" classification. The parties have referred to workers in the "Warehouse/Driver" classification as "full boat" employees, meaning that they enjoy maximum wages and fringe benefits. For simplicity we refer to "driver" and "grocery" as the two categories. The document that Murdoch sent Abramson (and the funds) in April 2008 provided that South Water Market would employ at least two drivers. After Castillo retired, it refused to provide more than one of its workers with the wages and fringe benefits of the driver classification. The pension and welfare funds contend in this suit under § 515 of the Employee Retirement Income Security Act (ERISA), 29 U.S.C. § 1145, that South Water Market must make delinquent contributions for a second driver position.

South Water Market's defense is that it never agreed to the terms that Murdoch drafted in April 2008. After a bench trial, the district judge agreed with South Water Market. Our narration comes from the district judge's findings of fact, which largely rest on the parties' stipulations. The basis of the district judge's ruling boils down to the observation that Abramson never signed Murdoch's draft and did not convey assent in any other way, such as by return email. All South Water Market did was comply with Murdoch's terms until August 2009, and performing according to someone else's proposal is not enough, the district judge ruled, to require an employer to continue doing so indefinitely.

The fundamental problem with the district court's approach is that the Labor Management Relations Act makes a written agreement essential to participation in a pension or welfare plan, 29 U.S.C. § 186(c)(5)(B), and ERISA provides that multi-employer pension and welfare funds can enforce these agreements as written. South Water Market does not contend that it wants to drop out of the pension and welfare plans, or that it did withdraw in September 2007. But if the April 2008 document is not the indispensable written agreement, then what is? At oral argument, South Water Market's lawyer replied: "the 2004 collective bargaining agreement." That won't do. The 2004 agreement expired by its own terms in 2007; what's more, the parties formally terminated it. Nothing remains except the April 2008 document. If South Water Market is to participate at all, those are the only available terms.

More than that: performance under a proposal is one means of giving assent to be bound. Bricklayers Local 21 of Illinois Apprenticeship and Training Program v. Banner Restoration, Inc., 385 F.3d 761, 766 (7th Cir.2004); Robbins v. Lynch, 836 F.2d 330, 332 (7th Cir.1988); Restatement (Second) of Contracts § 30. Murdoch reduced the terms to writing; South Water Market performed for more than a year, paying wages and making contributions at rates higher than those specified in the 2004 agreement. It now maintains that its payments to the funds did not really show assent to the two-drivers clause, because until August 2009 it had two drivers. Making fringe benefit contributions for two was only to be expected; until some difference developed between what South Water Market wanted and what the April 2008 document required, its performance was ambiguous. Yet South Water Market put all other terms of the April 2008 document into effect, and it is hard to see why an employer would do that if it thought the document merely a union's proposal. If it wanted to accept some clauses and reject others, it should have said so in April 2008. Yet its first protest came in response to the funds' August 2009 bills.

Pension and welfare funds are entitled to rely on the writings they receive. Central States Pension Fund v. Gerber Truck Service, Inc., 870 F.2d 1148 (7th Cir.1989) (en banc), analogizes them to holders in due course, not to simple third-party beneficiaries whose rights can be cut off at the contracting parties' whim. Usually they are not privy to negotiations between unions and employers; they cannot tell when one or the other(or both) had mental reservations. Pension and welfare funds set both benefit levels and contribution rates based on actuarial calculations, and those calculations depend on the terms of the written agreements that control coverage and eligibility. That's why funds can enforce the writings they receive. Gerber Truck Service held that a multi-employer pension fund can enforce a contract as written even though the union and the employer have a side agreement that certain parts of the contract will be ignored. See also, e.g., Central States Pension Fund v. Schilli Corp., 420 F.3d 663 (7th Cir.2005); Central States Pension Fund v. Joe McClelland, Inc., 23 F.3d 1256 (7th Cir.1994). Whatever reservations Abramson had were not conveyed to the funds until August 2009, much too late.

The judgment in favor of South Water Market is reversed. The case is remanded for calculation of how much it owes under the April 2008 document and entry of a judgment in that amount.