reserve S, R for 1-sorted,
  X for Subset of R,
  T for TopStruct,
  x for set;
reserve H for non empty multMagma,
  P, Q, P1, Q1 for Subset of H,
  h for Element of H;

theorem Th5:
  P c= Q implies P * h c= Q * h
proof
  assume
A1: P c= Q;
  let x be object;
  assume x in P * h;
  then ex g being Element of H st x = g * h & g in P by GROUP_2:28;
  hence thesis by A1,GROUP_2:28;
end;
