reserve X for set, a,b,c,x,y,z for object;
reserve P,R for Relation;

theorem
  R is reflexive iff id field R c= R
proof
  hereby
    assume
A1: R is reflexive;
    thus id field R c= R
    proof
      let a,b be object;
      assume [a,b] in id field R;
      then a in field R & a = b by RELAT_1:def 10;
      hence [a,b] in R by A1,Def1;
    end;
  end;
  assume
A2: id field R c= R;
  let a;
  assume a in field R;
  then [a,a] in id field R by RELAT_1:def 10;
  hence [a,a] in R by A2;
end;
