reserve F for Field,
  x for Element of F,
  V for VectSp of F,
  v for Element of V;

theorem
  x<>0.F implies x"*(x*v)=v
proof
  assume
A1: x<>0.F;
  x"*(x*v)=(x"*x)*v by Def15
    .=1.F*v by A1,Def10
    .=v;
  hence thesis;
end;
