reserve x for set,
  K for Ring,
  r for Scalar of K,
  V for LeftMod of K,
  a,b,a1,a2 for Vector of V,
  A,A1,A2 for Subset of V,
  l for Linear_Combination of A,
  W for Subspace of V,
  Li for FinSequence of Submodules(V);
reserve S1,S2 for Element of V..W;
reserve S for Element of V.W;

theorem Th20:
  for x being Vector of V/W ex a st x = a/W
proof
  let x be Vector of V/W;
  consider a such that
A1: x = a.W by Th15;
  take a;
  thus thesis by A1;
end;
