let K be non empty right_complementable Abelian add-associative right_zeroed associative well-unital distributive doubleLoopStr ; :: thesis: for V being VectSp of K
for W being Subspace of V
for w being Vector of (VectQuot V,W) holds
( w is Coset of W & ex v being Vector of V st w = v + W )
let V be VectSp of K; :: thesis: for W being Subspace of V
for w being Vector of (VectQuot V,W) holds
( w is Coset of W & ex v being Vector of V st w = v + W )
let W be Subspace of V; :: thesis: for w being Vector of (VectQuot V,W) holds
( w is Coset of W & ex v being Vector of V st w = v + W )
let w be Vector of (VectQuot V,W); :: thesis: ( w is Coset of W & ex v being Vector of V st w = v + W )
set qv = VectQuot V,W;
set cs = CosetSet V,W;
CosetSet V,W = the carrier of (VectQuot V,W) by Def6;
then w in { A where A is Coset of W : verum } ;
then consider A being Coset of W such that
A1: A = w ;
thus ( w is Coset of W & ex v being Vector of V st w = v + W ) by A1, VECTSP_4:def 6; :: thesis: verum