The Supreme Court’s decisions are sometimes opaque, and in this opinion, there is more than meets the eye. The court made it clear that the Fourth and Ninth Circuits were correct to suspend the ban for those nationals who have “bona fide” relationships here in the country. That is a long list: families, university students and professors, business owners and partners. In drawing that line, the Supreme Court handed a major victory to the plaintiffs who brought these cases — people with families affected by the ban and the Hawaii attorney general, who sued, in part, on behalf of the state’s university and its students.

But the real blow to the administration is hiding between the lines. Already, the court’s logic suggests that it is strongly leaning toward striking down much of the ban when it hears oral argument this October. To enjoin an executive order — as the Fourth and Ninth Circuits did — a court must be convinced that the policy has a “substantial likelihood” of being illegal. By keeping some of the injunctions against the travel ban in place pending the oral arguments scheduled for the fall, the Supreme Court was indicating that it agreed with the lower courts: The justices would not have kept the lower court’s injunctions against the ban at all unless they agreed that the ban, at least in part, was likely to be found illegal.

It now seems increasingly likely that the court will eventually strike down the ban if it is still in place in the fall. In fact, Mr. Trump’s own statements might lead to its invalidation. The Fourth Circuit held that the ban likely violates the Establishment Clause because it denigrates Muslims. In two amicus briefs I organized with Micah Schwartzman and Nelson Tebbe, which were signed by a large group of legal scholars, we explained to both the Fourth Circuit and the Supreme Court how we know the policy displays an intentional animus toward Muslims: Mr. Trump and his advisers told us. Rudy Giuliani told us on national television early in Mr. Trump’s term that the president wanted to enact a Muslim ban and that he had asked him to “make it legal.” While Mr. Trump’s lawyers tried to argue the contrary, Mr. Trump continued to admit in public that he preferred the first “politically incorrect” version of the ban, a reference to limits on Muslim immigration.

In the fall, when it will likely make a final ruling on the ban, the court may endorse the Fourth Circuit’s constitutional reasoning regarding the Establishment Clause as a justification for striking it down. Or it may take a second, easier path afforded to it by the Ninth Circuit: reversing the ban on the grounds that it violates a statutory prohibition on nationality-based discrimination in immigration. The advantage of this latter approach is that it could allow the court to avoid opening contentious constitutional debates. Either way, the decision this week made clear that the court found one of these two arguments against the ban likely to succeed.