
theorem Th59:
  for V be non empty ModuleStr over F_Complex, W be VectSp of
F_Complex for f be additiveFAF cmplxhomogeneousFAF Form of V,W for v be Vector
  of V, w be Vector of W holds (RQ*Form(f)).(v,w+RKer (f*')) = f.(v,w)
proof
  let V be non empty ModuleStr over F_Complex, W be VectSp of F_Complex, f be
additiveFAF cmplxhomogeneousFAF Form of V,W, v be Vector of V, w be Vector of W
  ;
  reconsider A=w+RKer(f*') as Vector of VectQuot(W,RKer (f*')) by VECTSP10:23;
  thus (RQ*Form(f)).(v,w+RKer (f*')) = ((RQForm(f*')).(v,A))*' by Def8
    .= (f*'.(v,w))*' by BILINEAR:def 21
    .= (f.(v,w))*'*' by Def8
    .= f.(v,w);
end;
