This section contains the nature of the case and procedural background.

P entered into a collective bargaining agreement in 1953 with Mills (D), employer. The agreement provided that there would be no strikes or work stoppages and that grievances would be handled pursuant to a specified procedure. The last step in the grievance procedure -- a step that could be taken by either party -- was arbitration. Grievances occurred and P requested arbitration, and D refused. P brought this suit in the District Court to compel arbitration. The District Court concluded that it had jurisdiction and ordered P to comply with the grievance arbitration provisions of the collective bargaining agreement. The Court of Appeals reversed the holding that the court had no authority founded either in federal or state law to grant the relief. P appealed.

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