Did Lucy cheated on Desi

There has been alot of speculation that Desi cheated on Lucy, but the only time that it was proven was right before "I Love Lucy" began. It has been recorded that Lucy and Desi were separated for much of the first decade of their marriage, due to his travels, alcohol abuse, and outside marital affairs. Lucy wanted to save their marriage, so they created the "I Love Lucy" pilot, hoping that the studio would be impressed and turn the pilot into a series. Lucy wanted to work side by side with Desi to keep him busy, hoping he wouldn't have time for other women, but also to keep track of him. They were set to get a divorce but reconciled right before the series began. Desi however did not change his ways and right after the last lucy-desi comedy hour "Lucy Meets the Moustache" was filmed Lucy filed for divorce.