
theorem Th32:
  for K be non empty multMagma for V,W be non empty ModuleStr over
K for v be Vector of V, w be Vector of W, a be Element of K for f be Form of V,
  W st f is homogeneousFAF holds f.(v,a*w) = a*f.(v,w)
proof
  let K be non empty multMagma;
  let V,W be non empty ModuleStr over K;
  let v be Vector of V, y be Vector of W, r be Element of K, f be Form of V,W;
  set F=FunctionalFAF(f,v);
  assume f is homogeneousFAF;
  then
A1: F is homogeneous;
  thus f.(v,r*y) = F.(r*y) by Th8
    .= r*F.y by A1
    .= r*f.(v,y) by Th8;
end;
