reserve A,X for non empty set;
reserve f for PartFunc of [:X,X:],REAL;
reserve a for Real;

theorem
  for X being set, R being Relation of X st R is_reflexive_in X holds rng R = X
proof
  let X be set, R be Relation of X such that
A1: R is_reflexive_in X;
  for x be object st x in X ex y be object st [y,x] in R
  proof
    let x be object such that
A2: x in X;
    take x;
    thus thesis by A1,A2,RELAT_2:def 1;
  end;
  hence thesis by RELSET_1:10;
end;
