
theorem rnginc:
  for f,g be Function holds
  (dom f c= dom g & for x be set st x in dom f holds f.x = g.x)
  implies rng f c= rng g
  proof
    let f,g be Function;
    assume that A2: dom f c= dom g and A2a: for x be set st x in dom f
    holds f.x = g.x;
    let x be object;assume x in rng f;then
    consider y be object such that A1: y in dom f & x = f.y by FUNCT_1:def 3;
    x = g.y by A2a,A1;
    hence x in rng g by FUNCT_1:3,A1,A2;
  end;
