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 Th16:
  a |^ g = b |^ g implies a = b
proof
  assume a |^ g = b |^ g;
  then g" * a = g" * b by GROUP_1:6;
  hence thesis by GROUP_1:6;
end;
