reserve T for TopSpace;
reserve A,B for Subset of T;
reserve T for non empty TopSpace;
reserve P,Q for Element of Topology_of T;
reserve p,q for Element of Open_setLatt(T);

theorem Th7:
  for p9,q9 being Element of Topology_of T st p=p9 & q=q9 holds p
  [= q iff p9 c= q9
proof
  let p9,q9 be Element of Topology_of T such that
A1: p=p9 and
A2: q=q9;
  hereby
    assume
A3: p [= q;
    p9 \/ q9 = p"\/"q by A1,A2,Def2
      .= q9 by A2,A3;
    hence p9 c= q9 by XBOOLE_1:7;
  end;
  assume
A4: p9 c= q9;
  p "\/" q = p9 \/ q9 by A1,A2,Def2
    .=q by A2,A4,XBOOLE_1:12;
  hence thesis;
end;
