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
for W being Subspace of V
for C being Coset of W holds
( 0. V in C iff C = the carrier of W )
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W being Subspace of V
for C being Coset of W holds
( 0. V in C iff C = the carrier of W )
let W be Subspace of V; :: thesis: for C being Coset of W holds
( 0. V in C iff C = the carrier of W )
let C be Coset of W; :: thesis: ( 0. V in C iff C = the carrier of W )
ex v being Element of V st C = v + W by Def6;
hence ( 0. V in C iff C = the carrier of W ) by Th48; :: thesis: verum