
theorem Th27:
  for V,W be non empty ModuleStr over F_Complex for v be Vector of
  V,w be Vector of W, a be Element of F_Complex for f be Form of V,W st f is
  cmplxhomogeneousFAF holds f.(v,a*w) = (a*')*f.(v,w)
proof
  let V,W be non empty ModuleStr over F_Complex, v1 be Vector of V, w be
  Vector of W, r be Element of F_Complex, f be Form of V,W;
  set F=FunctionalFAF(f,v1);
  assume f is cmplxhomogeneousFAF;
  then
A1: F is cmplxhomogeneous;
  thus f.(v1,r*w) = F.(r*w) by BILINEAR:8
    .= (r*')*F.w by A1
    .= (r*')*f.(v1,w) by BILINEAR:8;
end;
