let V be RealUnitarySpace; :: thesis: for W being Subspace of V
for v being VECTOR of V ex C being Coset of W st v in C
let W be Subspace of V; :: thesis: for v being VECTOR of V ex C being Coset of W st v in C
let v be VECTOR of V; :: thesis: ex C being Coset of W st v in C
reconsider C = v + W as Coset of W by RUSUB_1:def 5;
take C ; :: thesis: v in C
thus v in C by RUSUB_1:37; :: thesis: verum