reserve n for Element of NAT;
reserve i for Integer;
reserve G,H,I for Group;
reserve A,B for Subgroup of G;
reserve N for normal Subgroup of G;
reserve a,a1,a2,a3,b,b1 for Element of G;
reserve c,d for Element of H;
reserve f for Function of the carrier of G, the carrier of H;
reserve x,y,y1,y2,z for set;
reserve A1,A2 for Subset of G;

theorem Th14:
  for N being normal Subgroup of G holds a * N in Cosets N & N * a in Cosets N
proof
  let N be normal Subgroup of G;
  N * a in Right_Cosets N by GROUP_2:def 16;
  hence thesis by GROUP_2:def 15,GROUP_3:127;
end;
