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;

theorem Th28:
  f tolerates g iff f c= f +* g
proof
  thus f tolerates g implies f c= (f +* g)
  proof
    dom f \/ dom g = dom(f +* g) by Def1;
    then
A1: dom f c= dom(f +* g) by XBOOLE_1:7;
    assume f tolerates g;
    then for x being object st x in dom f holds (f +* g).x = f.x by Th15;
    hence thesis by A1,GRFUNC_1:2;
  end;
  thus thesis by Th27,PARTFUN1:54;
end;
