let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over 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 ModuleStr over 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 Th47;

hence the carrier of V is Coset of (Omega). V by Def6; :: thesis: verum

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over 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 Th47;

hence the carrier of V is Coset of (Omega). V by Def6; :: thesis: verum