reserve x,y,y1,y2 for object;
reserve GF for add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr,
  V,X,Y for Abelian add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital non
  empty ModuleStr over GF;
reserve a for Element of GF;
reserve u,u1,u2,v,v1,v2 for Element of V;
reserve W,W1,W2 for Subspace of V;
reserve V1 for Subset of V;
reserve w,w1,w2 for Element of W;

theorem Th36:
  (0).W = (0).V
proof
  the carrier of (0).W = {0.W} & the carrier of (0).V = {0.V} by Def3;
  then
A1: the carrier of (0).W = the carrier of (0).V by Def2;
  (0).W is Subspace of V by Th26;
  hence thesis by A1,Th29;
end;
