reserve X,Y for set,
  x,x1,x2,y,y1,y2,z for set,
  f,g,h for Function;
reserve M for non empty set;
reserve D for non empty set;
reserve P for Relation;
reserve O for Order of X;

theorem Th13:
  for A being set, R being Relation of A st R is_reflexive_in A
  holds dom R = A & field R = A
proof
  let A be set, R be Relation of A such that
A1: R is_reflexive_in A;
A2: A c= dom R
  proof
    let x be object;
    assume x in A;
    then [x,x] in R by A1;
    hence thesis by XTUPLE_0:def 12;
  end;
  hence dom R = A;
  thus field R = A \/ rng R by A2,XBOOLE_0:def 10
    .= A by XBOOLE_1:12;
end;
