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

theorem :: Theorem 1 (5H)
  for R being non empty mediate transitive RelStr,
      X being Subset of R holds
    UAp X = UAp (UAp X)
  proof
    let R be non empty mediate transitive RelStr;
    let X be Subset of R;
A0: UAp X c= UAp (UAp X) by ROUGHS_2:39;
    UAp (UAp X) c= UAp X by Th95H;
    hence thesis by A0,XBOOLE_0:def 10;
  end;
