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

theorem Th6:
  for X being set,x,y be object
  for R be Relation of X st X c= field R
  holds R reduces x,y & x in X implies [x,y] in R[*]
proof
  let X be set,x,y be object;
  let R be Relation of X such that
A1: X c= field R;
  assume that
A2: R reduces x,y and
A3: x in X;
  per cases by A2,REWRITE1:20;
  suppose
    [x,y] in R[*];
    hence thesis;
  end;
  suppose
A4: x = y;
    R[*] is_reflexive_in X by A1,Th5;
    hence thesis by A3,A4,RELAT_2:def 1;
  end;
end;
