theorem
  for t being FinSequence of INT holds
  ex u being FinSequence of REAL st t,u are_fiberwise_equipotent &
  u is non-increasing & u is FinSequence of INT &
  Sorting-Function.(fsloc 0 .--> t ) = fsloc 0 .--> u
proof
  let t be FinSequence of INT;
  consider u being FinSequence of REAL such that
A1: t,u are_fiberwise_equipotent and
A2: u is FinSequence of INT and
A3: u is non-increasing by RFINSEQ:33;
  reconsider u as FinSequence of INT by A2;
  set p = fsloc 0 .--> t;
  set q = fsloc 0 .--> u;
  [p, q] in Sorting-Function by A1,A3,Def7;
  then Sorting-Function.p = q by FUNCT_1:1;
  hence thesis by A1,A3;
end;
