
theorem

::Minkowski inequality - second version
  for V be VectSp of F_Complex for f be diagReR+0valued hermitan-Form of
V for v,w be Vector of V holds |. f.(v+w,v+w) .| <= (sqrt(|. f.(v,v) .|) + sqrt
  (|. f.(w,w) .|))^2
proof
  let V be VectSp of F_Complex, f be diagReR+0valued hermitan-Form of V, v1,w
  be Vector of V;
  set v3 = f.(v1,v1), v4 = f.(v1+w,v1+w), s1 = signnorm(f,v1), s2 = signnorm(f
  ,w), s12 = signnorm(f,v1+w);
A1: |.v4.| =s12 by Th41;
  s12 <= (sqrt(s1) + sqrt(s2))^2 & |.v3.| = s1 by Th41,Th47;
  hence thesis by A1,Th41;
end;
