theorem
  for V being ComplexLinearSpace, M being Subset of V, z1,z2 being
  Complex st (ex r1,r2 being Real st z1 = r1 & z2 = r2 & r1 >= 0 & r2 >= 0) & M
  is convex holds z1*M + z2*M = (z1 + z2)*M
proof
  let V be ComplexLinearSpace, M be Subset of V, z1,z2 be Complex;
  assume
  ( ex r1,r2 being Real st z1=r1 & z2=r2 & r1 >= 0 & r2 >= 0)& M is convex;
  hence z1*M + z2*M c= (z1 + z2)*M by Lm2;
  thus thesis by Th60;
end;
