theorem Th7:
  for A be Subset of G holds card A = card (g+A)
 proof
   let A be Subset of G;
   -g+(g+A) = (-g+g)+A by Th5
           .= 0.G+A by RLVECT_1:5
           .= A by Th6;
   then A1: card A c= card(g+A) by Lm4;
   card(g+A) c= card A by Lm4;
   hence thesis by A1;
 end;
