theorem Th37:
  p,q,r are_LinDep iff |{p,q,r}| = 0
  proof
    hereby assume p,q,r are_LinDep;
      then ex a,b,c st a*p + b*q + c*r = 0.TOP-REAL 3 &
      (a<>0 or b<>0 or c <>0) by ANPROJ_1:def 2;
      hence |{p,q,r}| = 0 by Th35;
    end;
    assume |{p,q,r}| = 0;
    then ex a,b,c st a*p + b*q + c*r = 0.TOP-REAL 3 &
    (a<>0 or b<>0 or c <>0) by Th36;
    hence p,q,r are_LinDep by ANPROJ_1:def 2;
  end;
