let V be ComplexLinearSpace; :: thesis: the carrier of V is Coset of (Omega). 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 ;
consider v being VECTOR of V;
A = v + ((Omega). V) by Th66;
hence the carrier of V is Coset of (Omega). V by Def9; :: thesis: verum