theorem Th2:
  for G being Group,N being Subgroup of G, x, y being Element of G
   st y in x * N holds x * N = y * N
proof
  let G be Group,N be Subgroup of G,x,y be Element of G;
  assume
A1:y in x * N;
  y in y * N by GROUP_2:108;
  then x * N meets y * N by A1,XBOOLE_0:3;
  hence thesis by GROUP_2:115;
end;
