reserve V for non empty RealLinearSpace;

theorem
for V be non empty RealLinearSpace holds 0.(V*') = (the carrier of V) --> 0
proof
  let V be non empty RealLinearSpace;
  consider Y be non empty VectSp of F_Real such that
  AS1:Y = RLSp2RVSp V & V*'= RVSp2RLSp Y*' by def2;
  0.(V*') = 0.(Y*') by AS1
         .= 0Functional Y by HAHNBAN1:def 10
         .= ([#]Y --> 0.(F_Real)) by HAHNBAN1:def 7;
  hence 0.(V*') = ((the carrier of V) --> 0) by AS1;
end;
