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 p,q being Function, A being set holds dom p c= A & dom q misses A
  implies (p +* q)|A = p
proof
  let p,q be Function, A be set;
  assume that
A1: dom p c= A and
A2: dom q misses A;
  thus (p +* q )|A = p|A by A2,Th72
    .= p by A1,RELAT_1:68;
end;
