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 Function st dom f c= dom g holds f tolerates g
  iff for x being object st x in dom f holds f.x = g.x
proof
  let f,g be Function;
  assume dom f c= dom g;
  then dom f /\ dom g = dom f by XBOOLE_1:28;
  hence thesis;
end;
