The phrase "after they provided" is correct and usable in written English.
It can be used to indicate a sequence of events where something occurs following the act of providing information or resources.
Example: "After they provided the necessary documents, the application was processed without delay."
Alternatives: "after they supplied" or "after they delivered".
Last year, Greece's foreign lenders imposed austerity measures after they provided a first round of aid.
Another evening we enjoyed dinner at the more elegant Pink Elephant -- after they provided me with the standard-issue sport coat.
Two firefighters who have been suspended amid allegations of sexual misconduct with a woman in a Bronx firehouse were threatened with criminal perjury charges yesterday after they provided false testimony, officials said.
Sergei Duvanov, a well-known journalist here, said access to his Web site, www.inkar.info, and three other sites was denied after they provided transcripts and recordings of what were described as top officials' telephone conversations about the Aliyev case.
The lawyer, Rusty Hardin, said that prosecutors had indicated to the three witnesses that they might face indictment after they provided statements to investigators about last fall's destruction of documents related to Enron.
Darren Currie, the Barnet caretaker manager, praised the fearlessness of his side after they provided the biggest shock of the day in the FA Cup to reach the fourth round by beating Sheffield United at Bramall Lane.
First, patients should be evaluated and treated only after they provide informed consent, unless they are incompetent.
Under the World Anti-Doping Code, athletes can be sanctioned for a violation up to eight years after they provide their urine or blood samples for a drug test.
Traditional sites bombard consumers with phone calls or emails after they provide their contact information.
Alan Luks, a professor at Fordham University, found that people experience a "Helper's High" after they provide assistance.
MSM individuals were interviewed and their eligibility was confirmed through screening questionnaires and HIV testing after they provide written informed consent to the study.
