reserve x,z for set;
reserve k for Element of NAT;
reserve D for non empty set;
reserve X for set;
reserve p,r for relation;
reserve a,a1,a2,b for FinSequence;
reserve a,b for FinSequence of D;
reserve p,r for Element of relations_on D;

theorem
  X c= r implies X is Element of relations_on D
proof
  assume
A1: X c= r;
  then
A2: for a,b st a in X & b in X holds len a = len b by Def7;
  r c= D* by Def7;
  then X c= D* by A1;
  hence thesis by A2,Def7;
end;
