theorem Th55:
  (0).W = (0).V
proof
  the carrier of (0).W = {0.W} & the carrier of (0).V = {0.V} by Def9;
  then
A1: the carrier of (0).W = the carrier of (0).V by Def8;
  (0).W is Subspace of V by Th46;
  hence thesis by A1,Th49;
end;
