reserve n,m,k for Nat,
  x,y for set,
  r for Real;
reserve C,D for non empty finite set,
  a for FinSequence of bool D;

theorem Th24:
  for F be PartFunc of D,REAL, A be RearrangmentGen of C st F is
  total & card C = card D holds FinS(Rlor(F,A),C) = FinS(F,D)
proof
  let F be PartFunc of D,REAL, B be RearrangmentGen of C;
  assume
A1: F is total & card C = card D;
  then
A2: Rlor(F,B), FinS(F,D) are_fiberwise_equipotent by Th23;
A3: dom Rlor(F,B) = C by A1,Th20;
  then (Rlor(F,B))|C = Rlor(F,B) by RELAT_1:68;
  hence thesis by A2,A3,RFUNCT_3:def 13;
end;
