Mr Smith’s office argues that a speedy trial is in the public interest.
That interest, the prosecutors say, is “of particular significance here, where the defendant, a former president, is charged with conspiring to overturn the legitimate results of the 2020 presidential election, obstruct the certification of the election results, and discount citizens’ legitimate votes.”
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Prosecutors believe it will take about four to six weeks to put forward the bulk of their case against Trump at trial.
But the former president’s lawyers have already said they will try to slow things down.
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Trump last week pleaded not guilty to charges over the alleged election conspiracy.
He says he is innocent and has portrayed the investigation as politically motivated.
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Trump: ‘A very sad day for America’
The charges
Trump is facing four criminal charges relating to attempts to overturn the 2020 election result as prosecutors try to tie him to the January 6 storming of the US Capitol building by his supporters. They are:
• Conspiracy to defraud the US
• Conspiracy to obstruct an official proceeding
• Obstruction of, and attempt to obstruct, an official proceeding
• Conspiracy against rights.
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QAnon Shaman cut off by Sky News presenter
Other cases
Mr Trump’s latest charges add to his ongoing legal woes, with recent court appearances in Miami and New York.
In Miami, Mr Trump pleaded not guilty to allegations that he unlawfully kept national security documents when he left office and lied to officials, trying to recover them.
He also pleaded not guilty in New York to 37 charges, relating to falsifying business records “in order to conceal damaging information and unlawful activity from American voters before and after the 2016 election”.
Mr Trump is also counter-suing E. Jean Carroll, who alleged he raped her in the 1990s – he was found guilty of sexually assaulting and defaming her, but not raping Ms Carroll in a civil case.