theorem
  W1 is Subspace of W2 implies v + W1 c= v + W2
proof
  assume
A1: W1 is Subspace of W2;
  let x be object;
  assume x in v + W1;
  then consider u such that
A2: u in W1 and
A3: x = v + u by RLSUB_1:63;
  u in W2 by A1,A2,RLSUB_1:8;
  hence thesis by A3,RLSUB_1:63;
end;
