
theorem Th16:
  for X be non empty set, f,g be PartFunc of X,ExtREAL st f is
  without-infty & g is without-infty holds dom(f+g)=dom f /\ dom g
proof
  let X be non empty set;
  let f,g be PartFunc of X,ExtREAL;
  assume that
A1: f is without-infty and
A2: g is without-infty;
  not -infty in rng g by A2;
  then
A3: g"{-infty} = {} by FUNCT_1:72;
  not -infty in rng f by A1;
  then f"{-infty} = {} by FUNCT_1:72;
  then f"{+infty} /\ g"{-infty} \/ f"{-infty} /\ g"{+infty} = {} by A3;
  then dom(f+g) = (dom f /\ dom g)\{} by MESFUNC1:def 3;
  hence thesis;
end;
