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 Th4:
  P c= P1 & Q c= Q1 implies P * Q c= P1 * Q1
proof
  assume
A1: P c= P1 & Q c= Q1;
  let x be object;
  assume x in P * Q;
  then ex g, t being Element of H st x = g * t & g in P & t in Q;
  hence thesis by A1;
end;
