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
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 VectSp-like Abelian add-associative right_zeroed VectSpStr of 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 Th63; :: thesis: verum