ESPN legal analyst Lester Munson explains why the NFL's hiring of Paul Clement sends a strong message to Tom Brady and the NFLPA. (2:14)

The NFL has hired one of the nation's most successful appellate attorneys to fight the court decision that reversed New England Patriots quarterback Tom Brady's four-game suspension for Deflategate.

Paul Clement, who has argued more U.S. Supreme Court cases than any other lawyer, filed papers on behalf of the NFL on Monday in the U.S. Court of Appeals for the Second Circuit in New York. Clement, who also defended the NFL in the class-action concussion lawsuit, has argued in the nation's highest court against Obamacare and in support of the Defense of Marriage Act, among other cases.

In early September, U.S. District Judge Richard Berman said NFL commissioner Roger Goodell used "his own brand of industrial justice" to discipline Brady for an alleged conspiracy to deflate footballs below the allowable limit during the previous season's AFC Championship Game.

Berman cited "several significant legal deficiencies'' in the league's handling of the controversy, including no advanced notice of potential penalties, refusal to produce a key witness and the first-ever discipline of a player based on a finding of "general awareness'' of someone else's wrongdoing.

"Because there was no notice of a four-game suspension in the circumstances presented here, Commissioner Goodell may be said to have 'dispensed his own brand of industrial justice,''' Berman wrote. He said a player's right to notice was "at the heart'' of the league's collective bargaining agreement with the NFL Players Association "and, for that matter, of our criminal and civil justice systems.''

"The court finds that Brady had no notice that he could receive a four-game suspension for general awareness of ball deflation by others,'' the judge wrote.

The NFL appealed Berman's decision immediately. On Monday, the league filed a 59-page brief outlining its appeal of Berman's decision.

The league argues in its brief that Goodell acted within his discretion under the CBA to suspend the Patriots quarterback for four games and the district court that overturned the decision "vastly exceeded" the narrow bounds of its review.

NFL lawyers also told the appeals court that Berman reached an "inexplicable'' conclusion when he determined that the league failed to adequately warn Brady of the potential suspension and made errors in its investigation, such that he was required to nullify the penalty.

The brief maintains that "significant evidence linked [Brady] to the deflation scheme," which was "aimed at gaining an unfair competitive advantage on the field." It says the scheme was devised to "avoid detection by game officials."

The lawyers wrote that the judge's finding that the league's conclusions were so far outside the bounds of what the contract allows that Goodell's decision must be nullified "is unfathomable.''

"The district court egregiously overstepped the bounds of its proper role,'' the NFL said. "Where lower courts have committed a similar error, appellate courts have not hesitated to reverse. The court should do so here.''

Brady and the NFLPA are due to respond in December, with Clement and the league offering a final response after that. A decision is expected in the spring.

Goodell, in an appearance Tuesday on ESPN Radio's Mike & Mike, reiterated that the NFL's decision to appeal is all about the league's rights in the CBA.

"I'm not spending any time on this issue, but it is important for us to know what we bargained for, what we agreed to in our collective bargaining agreement and make sure those processes that are agreed to in our collective bargaining agreement are followed," he said. "And so, we're not going to allow that kind of a decision to stand when we think it's in conflict with our collective bargaining agreement. That is the issue. It has nothing to do with any individual player or anyone else. It has something to do with Judge Berman's decision, and that's what we're appealing."

The Associated Press contributed to this report.