theorem Th23:
  (f +* g)|(dom g) = g
proof
  dom f \/ dom g = dom(f +* g) by Def1;
  then
A1: dom((f +* g)|(dom g)) = dom g by RELAT_1:62,XBOOLE_1:7;
  for x being object st x in dom g holds ((f +* g)|(dom g)).x = g.x
  proof
    let x be object;
    x in dom g implies (f +* g).x = g.x by Th13;
    hence thesis by A1,FUNCT_1:47;
  end;
  hence thesis by A1;
end;
