Story highlights A Cairo court overturns a rule allowing the military to arrest civilians

Mohamed Morsi's adviser says he will pick a woman and a Christian as vice presidents

Morsi has begun assembling a new government

Ahmed Shafik will establish a new political party in Egypt, his office says

Egypt's first democratically elected president, Mohamed Morsi, will appoint a woman as one of his vice presidents and a Christian as another, his policy adviser told CNN.

"For the first time in Egyptian history -- not just modern but in all Egyptian history -- a woman will take that position," Ahmed Deif told CNN's Christiane Amanpour on Monday. "And it's not just a vice president who will represent a certain agenda and sect, but a vice president who is powerful and empowered and will be taking care of critical advising within the presidential Cabinet."

The news came as the man Morsi beat for the presidency, Ahmed Shafik, left Egypt for Abu Dhabi, and as Cairo's administrative court overturned a rule that allowed the military to arrest people without a warrant.

Though Morsi had previously argued for banning women from the presidency, he said before the election that as president he would stand for women's rights.

"The role of women in Egyptian society is clear," Morsi told CNN weeks before the runoff election. "Women's rights are equal to men. Women have complete rights, just like men. There shouldn't be any kind of distinction between Egyptians except that ... based on the constitution and the law."

The Islamist figure, a Muslim Brotherhood leader, also promised to safeguard the rights of minorities.

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Egypt "definitely" will not be an "Islamic Republic," Deif said Monday.

Morsi moved into his offices Monday, said Jihad Haddad, an adviser to the transition team.

He began the work of assembling a new government -- one of the powers he maintains after the military junta running the country recently slashed the presidency's reach.

The process of picking people to serve in the Cabinet "won't end in a day," Haddad said.

Shafik, who lost in the runoff election to Morsi, left the country Tuesday for the United Arab Emirates, his attorney and a Cairo airport official said.

He traveled to Abu Dhabi, Cairo airport official Mohamed Sultan said.

He is not fleeing the country, Shafik's attorney, Showee Elsayed, told CNN.

While legal petitions accusing Shafik of corruption were submitted in April, prosecutors have not taken legal action on them, so "there are absolutely no legal cases pending" against him, Elsayed said.

Shafik was the final prime minister to serve under President Hosni Mubarak before he was ousted.

Shafik's office said Tuesday he "will establish a new political party upon his return from the UAE and Saudi Arabia, where he is on private visits."

He and his two daughters will perform Umrah, an Islamic religious pilgrimage to Mecca.

Meanwhile, Cairo's administrative court, which hears civilian complaints against the government, rejected a controversial rule Tuesday that the Ministry of Justice had established before the election.

The rule stated that military personnel and intelligence forces could arrest civilians without a warrant. The right to arrest civilians had previously been reserved for police officers, the state-run Ahram news agency reported.

The court also decided that, on September 1, it will look into legal petitions filed against the Supreme Council of the Armed Forces over its decision to cancel the constitutional committee, which had been charged by the parliament before it was dissolved with drafting a new constitution.

The court decided that on July 7, it will look into legal petitions filed to stop recently issued constitutional articles by SCAF that limit the powers of the president.

And on July 10, the court will look into legal petitions filed against the decision to dissolve parliament.

They were among 14 legal complaints filed about the rule by various individuals and groups, including the Muslim Brotherhood.