reserve n,m for Nat;

theorem
  for f being real-valued FinSequence holds sort_a (-f) = - (sort_d f)
proof
  let f be real-valued FinSequence;
  -f,sort_a(-f) are_fiberwise_equipotent by Def6;
  then
A1: --f,-sort_a(-f) are_fiberwise_equipotent by Th25;
  -sort_a (-f) is non-increasing by Th23;
  then -sort_a (-f)=sort_d f by A1,Def5;
  hence thesis;
end;
