theorem Th30:
  dim V = dim (Omega).V
proof
  consider I being finite Subset of V such that
A1: I is Basis of V by Def1;
A2: (Omega).V = the RLSStruct of V by RLSUB_1:def 4
    .= Lin(I) by A1,RLVECT_3:def 3;
  card I = dim V & I is linearly-independent by A1,Def2,RLVECT_3:def 3;
  hence thesis by A2,Th29;
end;
