 reserve x,y,z,t for object,X,Y,Z,W for set;
 reserve R,S,T for Relation;

theorem
  id X c= R implies id X c= R~
proof
  assume
A1: id X c= R;
  for x being object holds x in X implies [x,x] in R~
  proof
    let x be object;
    assume x in X;
    then [x,x] in id X by RELAT_1:def 10;
    hence thesis by A1,RELAT_1:def 7;
  end;
  hence thesis by RELAT_1:47;
end;
