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

theorem :: Theorem 1 (5L)
  for R being non empty mediate transitive RelStr,
      X being Subset of R holds
    LAp X = LAp (LAp X)
  proof
    let R be non empty mediate transitive RelStr;
    let X be Subset of R;
A0: LAp X c= LAp (LAp X) by Th95L;
    LAp (LAp X) c= LAp X by ROUGHS_2:40;
    hence thesis by A0,XBOOLE_0:def 10;
  end;
