theorem
  x*v = 0.V iff x = 0.F or v = 0.V
proof
  x*v = 0.V implies x = 0.F or v = 0.V
  proof
    assume x*v = 0.V;
    then
A1: (x"*x)*v = x"*(0.V) by VECTSP_1:def 16
      .= 0.V by VECTSP_1:14;
    assume x<> 0.F;
    then 0.V = (1_F)*v by A1,Th9;
    hence thesis by VECTSP_1:def 17;
  end;
  hence thesis by VECTSP_1:14;
end;
