reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th6:
  H1 is Subgroup of H2 implies a * H1 c= a * H2 & H1 * a c= H2 * a
proof
  assume H1 is Subgroup of H2;
  then the carrier of H1 c= the carrier of H2 by GROUP_2:def 5;
  hence thesis by Th4;
end;
