
theorem Th26:
  for V be VectSp of F_Complex, f be antilinear-Functional of V
  for A be Vector of VectQuot(V,Ker (f*')), v be Vector of V st A = v+Ker (f*')
  holds (QcFunctional(f)).A = f.v
proof
  let V be VectSp of F_Complex, f be antilinear-Functional of V;
  let A be Vector of VectQuot(V,Ker (f*')), v be Vector of V;
  assume
A1: A = v+Ker (f*');
  the carrier of (Ker (f*')) = ker (f*') by VECTSP10:def 11
    .= ker f by Th23;
  hence thesis by A1,VECTSP10:def 12;
end;
