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 Th29:
  for W1,W2 being strict Subspace of V st the carrier of W1 = the
  carrier of W2 holds W1 = W2
proof
  let W1,W2 be strict Subspace of V;
  assume the carrier of W1 = the carrier of W2;
  then W1 is Subspace of W2 & W2 is Subspace of W1 by Th27;
  hence thesis by Th25;
end;
