reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;

theorem
  for f,g being Function , A being set holds dom f misses A implies
  (f +* g)|A = g|A
proof
  let f,g be Function , A be set;
  assume dom f misses A;
  then dom f /\ A = {};
  then dom (f|A) = {} by RELAT_1:61;
  then f|A = {};
  hence (f +* g)|A = {} +* g|A by Th71
    .= g|A;
end;
