let V be RealLinearSpace; :: thesis: the carrier of V is Coset of (Omega). V
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 = the VECTOR of V + ((Omega). V) by Th46;
hence the carrier of V is Coset of (Omega). V by Def6; :: thesis: verum