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 VectSp-like 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 VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: the carrier of V is Coset of (Omega). V
the carrier of V c= the carrier of V ;
then reconsider A = the carrier of V as Subset of V ;
consider v being Element of V;
A = v + ((Omega). V) by Th62;
hence the carrier of V is Coset of (Omega). V by Def6; :: thesis: verum