reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  for f,g being PartFunc of X,Y for h being Function st f tolerates h &
  g c= f holds g tolerates h
proof
  let f,g be (PartFunc of X,Y),h be Function such that
A1: f tolerates h and
A2: g c= f;
A3: dom g c= dom f by A2,RELAT_1:11;
  let x be object;
  assume
A4: x in dom g /\ dom h;
  then
A5: x in dom g by XBOOLE_0:def 4;
  then
A6: f.x = g.x by A2,GRFUNC_1:2;
  x in dom h by A4,XBOOLE_0:def 4;
  then x in dom f /\ dom h by A5,A3,XBOOLE_0:def 4;
  hence thesis by A1,A6;
end;
