theorem
  v*x = 0.V iff x = 0.F or v = 0.V
proof
  v*x = 0.V implies x = 0.F or v = 0.V
  proof
    assume v*x = 0.V;
    then
A1: v*(x*x") = (0.V)*x" by Def8
      .= 0.V by Th32;
    assume x<>(0.F);
    then 0.V = v*(1_F) by A1,Th9;
    hence thesis by Def8;
  end;
  hence thesis by Th32;
end;
