let R be Ring; :: thesis: for V being LeftMod of R
for W being Submodule of V
for v being Vector of V ex C being Coset of W st v in C
let V be LeftMod of R; :: thesis: for W being Submodule of V
for v being Vector of V ex C being Coset of W st v in C
let W be Submodule 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 VECTSP_4:def 6;
take C ; :: thesis: v in C
thus v in C by Th58; :: thesis: verum