The Rule of Four means four of the nine justices must agree to hear a case in order for it to be accepted on appeal. If four or more justices think the case is worth the Court's time, then the Supreme Court will issue a writ of certiorari to the lower court ordering them to send the case files to the Supreme Court, and the case will be placed on the docket.
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ALL lower courts, both state and federal, can be reviewed by the Supreme Court. Every court in the nation is subordinate to the US Supreme Court.
The Judicial Branch in general, and the US Supreme Court, in particular, were perceived as weak.
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If a state court declares a state law unconstitutional, the state will probably appeal the case to the state supreme court. If a state court declares a federal law unconstitutional, the losing party in the case will appeal the decision in the federal courts. The case could ultimately be heard by the US Supreme Court; however, if a lower court reverses the state court's decision and either the appropriate US Court of Appeals Circuit Court or US Supreme Court decline to consider the case, the decision of the lower federal court would be final. The US Supreme Court is the ultimate arbiter of constitutionality.
No, Justice Sonia Sotomayor is the third woman appointed to the US Supreme Court. President Reagan appointed Sandra Day O'Connor as the first woman to serve on the Court in 1981; President Clinton appointed Ruth Bader Ginsberg in 1993; President Obama appointed Sonia Sotomayor in 2009 and Elena Kagan in 2010. In all, four women have served on the US Supreme Court; three are still active.