let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF holds the carrier of V is Coset of (Omega). V
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: the carrier of V is Coset of (Omega). V
set v = the Element of V;
the carrier of V c= the carrier of V ;
then reconsider A = the carrier of V as Subset of V ;
A = the Element of V + ((Omega). V) by Th62;
hence the carrier of V is Coset of (Omega). V by Def6; :: thesis: verum