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;
reserve G for Group,
  A, B for Subset of G,
  a for Element of G;

theorem Th7:
  a in A" iff a" in A
proof
  a"" = a & A"" = A;
  hence thesis;
end;

Lm1: A c= B implies A" c= B"
proof
  assume
A1: A c= B;
  let a be object;
  assume a in A";
  then ex g being Element of G st a = g" & g in A;
  hence thesis by A1;
