
theorem Th29:
  for K be Field, V be non trivial VectSp of K for v be Vector of
  V, a be Scalar of V for W be Linear_Compl of Lin{v} st v <> 0.V holds (
  coeffFunctional(v,W)).(a*v) = a
proof
  let K be Field, V be non trivial VectSp of K, v be Vector of V, a be Scalar
  of V, W be Linear_Compl of Lin{v};
  assume
A1: v <> 0.V;
  set cf = coeffFunctional(v,W);
  thus cf.(a*v) = a*cf.v by HAHNBAN1:def 8
    .= a*(1_K) by A1,Def8
    .= a;
end;
