
theorem Th57:
  for V be VectSp of F_Complex, f be diagReR+0valued diagRvalued
Form of V,V for v be Vector of V st Re (f.(v,v))= 0 holds f.(v,v)= 0.F_Complex
proof
  let V be VectSp of F_Complex, f be diagReR+0valued diagRvalued Form of V,V,
  v be Vector of V;
  assume
A1: Re (f.(v,v)) = 0;
  Im (f.(v,v)) = 0 by Def6;
  then f.(v,v) = 0 + 0*<i> by A1,COMPLEX1:13;
  hence thesis by COMPLFLD:7;
end;
