 reserve Omega for non empty set;
 reserve r for Real;
 reserve Sigma for SigmaField of Omega;
 reserve P for Probability of Sigma;

theorem Th2:
  for f,g be Function holds rng (f*g) c= rng (f|(rng g))
  proof
    let f,g be Function;
    let y be object;
    assume y in rng(f*g);then
    consider x be object such that
A1: x in dom (f*g) & y=(f*g).x by FUNCT_1:def 3;
A2: x in dom g & g.x in dom f by A1,FUNCT_1:11;
    reconsider z=g.x as set;
    f.z in rng (f|(rng g)) by A2,FUNCT_1:3,50;
    hence thesis by A1,FUNCT_1:12;
  end;
