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 Th30:
  for F be PartFunc of D,REAL, A be RearrangmentGen of C st F is
  total & card D = card C holds len FinS(Rland(F,A),C) = card C & 1<=len FinS(
  Rland(F,A),C)
proof
  let F be PartFunc of D,REAL, B be RearrangmentGen of C;
  set p = Rland(F,B);
  assume F is total & card D = card C;
  then
A1: dom p = C by Th12;
  then
A2: p|C = p by RELAT_1:68;
  hence len FinS(p,C) = card C by A1,RFUNCT_3:67;
  0+1<=card C by NAT_1:13;
  hence thesis by A1,A2,RFUNCT_3:67;
end;
