reserve V for RealLinearSpace;
reserve p,q,r,u,v,w,y,u1,v1,w1 for Element of V;
reserve a,b,c,d,a1,b1,c1,a2,b2,c2,a3,b3,e,f for Real;

theorem Th5:
  u,v,w are_LinDep implies u,w,v are_LinDep & v,u,w are_LinDep & w
  ,v,u are_LinDep & w,u,v are_LinDep & v,w,u are_LinDep
proof
  assume u,v,w are_LinDep;
  then consider a,b,c such that
A1: a*u + b*v + c*w = 0.V and
A2: a<>0 or b<>0 or c <>0;
  a*u + c*w + b*v = 0.V & b*v + c*w + a*u = 0.V by A1,RLVECT_1:def 3;
  hence thesis by A1,A2;
end;
