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} holds f tolerates g
proof
  let f,g be PartFunc of X,{y};
  let x be object;
  assume
A1: x in dom f /\ dom g;
  then x in dom f by XBOOLE_0:def 4;
  then
A2: f.x = y by Th20;
  x in dom g by A1,XBOOLE_0:def 4;
  hence thesis by A2,Th20;
end;
