theorem
  the carrier of V is Coset of (Omega).V
proof
  set v = the VECTOR of V;
  the carrier of V is Subset of V iff the carrier of V c= the carrier of V;
  then reconsider A = the carrier of V as Subset of V;
  A = v + (Omega).V by Th46;
  hence thesis by Def6;
end;
